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Lesson 17:
Real Estate Math
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Principles of California
Real Estate
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aFAVAlSouHBBxb6jKjA4bSqBwNGpBKxOparCalYVUrE+VYGAgAQhXqFKCIthbNewaMdikIoBwVy6 U+XeRSABAdy7EjDAnZF3Bl8MDzAMNiwBMeDEgf0hVsxXgoa/EgICADs= ------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0002.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
Solving Math Problems
Four steps=
<= span style=3D'font-weight:bold'>1.Read the question.
<= span style=3D'font-weight:bold'>2.Write down the formula. <= /div>
3.Substitute the numbers in
the problem into the formula.
<= span style=3D'font-weight:bold'>4.Calculate the answer.
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Solving Math Problems
Using formulas
» Each of these choices expresses the same formula, but in a way that lets you solve it for A, B, or C:
»A =3D B × C
»B =3D A ÷ C
»C =3D A ÷ B
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Solving Math Problems
Using formulas
»Isolate the unknown.
—The unknown is the element that you’re trying to determine.
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Solving Math Problems
Using formulas
»Isolate the unknown.
—The unknown is the element that you’re trying to determine.
—The unknown should always sit alone on one side of the equals sign.=
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Solving Math Problems
Using formulas
»Isolate the unknown.
—The unknown is the element that you’re trying to determine.
—The unknown should always sit alone on one side of the equals sign.
—All the information that you already know should be on the other s= ide.
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Solving Math Problems
Usi= ng formulas
»= Example: What is the length = of a property that is 9,000 square feet and 100 feet wide?
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Solving Math Problems
Usi= ng formulas
» Example: What is the length of a property that is 9,000 square feet and 100 feet wide?
—The formula for area is A =3D L × = W.
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Solving Math Problems
Usi= ng formulas
» Example: What is the length of a property that is 9,000 square feet and 100 feet wide?
—The formula for area is A =3D L × W.
—L is the unkn= own, so switch the formula to L =3D A ÷ W.
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Solving Math Problems
Usi= ng formulas
» Example: What is the length of a property that is 9,000 square feet and 100 feet wide?
—The formula for area is A =3D L × W.
—L is the unkn= own, so switch the formula to L =3D A ÷ W.
» 90 =3D 9,000 ÷ 100
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Decimal Numbers
Con= verting fraction to decimal
»Calculators use only decimals, not fractions.
»<= /span>If a problem contains a fraction, convert it to a decimal:<= /div>
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Decimal Numbers
Con= verting fraction to decimal
»Calculators use only decimals, not fractions.
»<= /span>If a problem contains a fraction, convert it to a decimal:
—Divide the top number (the numerator) by the bottom number (the denominator)= .
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Decimal Numbers
Con= verting fraction to decimal
»Calculators use only decimals, not fractions.
»<= /span>If a problem contains a fraction, convert it to a decimal:
—Divide the top number (the numerator) by the bottom number (the denominator).
§     1/4 =3D 1 ÷ 4 =3D 0.25
§     1/3 =3D 1 ÷ 3 =3D 0.333
§     5/8 =3D 5 ÷ 8 =3D 0.625
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Decimal Numbers
Converting decima= l to percentage
»To convert a decimal to a percentage, move <= span style=3D'position:absolute;top:31.5%;left:7.3%;width:99.06%;height:6.75%'>= the decimal point two numbers to the right and add a percent sign.
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Decimal Numbers
Converting decima= l to percentage
»<= /span>To convert a decimal to a percentage, move the decimal point two numbe= rs to the right and add a percent sign.
§           0.02 =3D 2%
§           0.80 =3D 80%
§           1.23 =3D 123%
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= »<= /span>To convert a percentage to a decimal, reverse the process:
—Move the deci= mal point two numbers to
the left and remove the percent sign.
Decimal Numbers
Converting percen= tage to decimal
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= »<= /span>To convert a percentage to a decimal, reverse the process:
—Move the deci= mal point two numbers to
the left and remove the percent sign.
»    2% =3D 0.02
»    80% =3D 0.8
»    123% =3D 1.23
Decimal Numbers
Converting percen= tage to decimal
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Summary
Solving Math Pro= blems
»Read problem
»<= /span>Write formula
  and isolate the
  unknown
»Substitute
»Calculate
»=
»
»
»Fractions
»Decimal numbers
»Percentages
»Conversion
»
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Area Problems
Formula: A =3D L= × W
» To determine
the area of a <= span style=3D'position:absolute;top:38.5%;left:7.3%;width:41.01%;height:6.75%'>= rectangular or square space,
use this formula: =
»    A =3D L = × W
Area
Width
Length
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Area Problems
» You might also be asked to factor other = elements into an area problem, such as:
—cost per square foot, <= /div>
—rental rate, or
—the amount of the broker’s commiss= ion.
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Area Problems
Exa= mple
»= An office is 27 feet wide by= 40 feet long.
It rents for $2 per square foot per month. = How much is the monthly rent?
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Area Problems
Exa= mple
» An office is 27 feet wide by 40 feet long.
It rents for $2 per square foot per month. = How much is the monthly rent?
—Part 1: Calcu= late area
» A =3D 27 feet × 40 feet
» A =3D 1,080 square feet
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Area Problems
Exa= mple
»= An office is 27 feet wide by= 40 feet long.
It rents for $2 per square foot per month. = How much is the monthly rent?
—Part 1: Calcu= late area
» A =3D 27 feet × 40 feet
» A =3D 1,080 square feet
—Part 2: Calcu= late rent
§ Rent =3D 1,080 × $2
» Rent =3D $2,160
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Area Problems
Square yards
»<= /span>Some problems express area in square yards rather than square feet. &#= 13;
»Remember: 1 squ= are yard =3D 9 square feet
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Area Problems
Square yards
»<= /span>Some problems express area in square yards rather than square feet. &#= 13;
»Remember: 1 squ= are yard =3D 9 square feet
—1 yard is 3 feet
—1 square yard measures 3 feet on e= ach side
—3 feet × 3 feet =3D 9 square feet<= /span>
------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0013.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
Area Problems
Triangle formula= : A =3D ½ B × H
» To determine the= = area of a right triangle, use this formula:
»    A =3D ½ = B × H
<= ![if !vml]>3D"CP17_032_01"
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Area Problems
Triangle formula= : A =3D ½ B × H
» To determine the= = area of a right triangle, use this formula:
»    A =3D ½ = B × H
»
» Right triangle: =
a triangle with a
90º angle
<= ![if !vml]>3D"CP17_032_01"
------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0014.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
»Visualize a rectangle, then cut it in half = <= span style=3D'font-size:94%'>diagonally. What’s left is a right triangle.
Area of a Triangle
------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0191.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
<= span style=3D'font-size:94%'>»Visualize a rectangle, then cut it in half diagonally. What’s left is a right triangle.
—If you’re finding the area of a right triangle, it= doesn’t matter at what point in the formula you cut the rectangle in half.
Area of a Triangle
------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0192.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
»Visualize a rectangle, then cut it in half = = diagonally. What’s left is a right triangle. <= /span>
—If you’re finding the area of a right triangle, it doesn’t matter at what point in the formula you cut the rectangle in half. <= /div>
—In other = words, any of these variations will reach the same result:
—                         A =3D ½ B × H&#= 13;
—                         A =3D B × ½ H&#= 13;
—                         A =3D (B × H) ÷= 2
Area of a Triangle
------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0015.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
»= A triangular lot is 140 fe= et long and 50 feet wide at its= base. What is the area?
<= ![if !vml]>3D"CP17_034_01"=
Triangles
Example
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» A triangular lot= is = 140 feet long and 50 = feet wide at its base. What is the area?
—Do the calculation in any of the following ways to get the correct <= /span>answer.
<= ![if !vml]>3D"CP17_034_01"=
Triangles
Example
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» A triangular lot= is = 140 feet long and 50 = feet wide at its base. What is the area?
» Variation 1:= 3;
» A =3D (½ × 50) × 140
» A =3D 25 × 140&= #13;
» A =3D 3,500 sq.= feet
<= ![if !vml]>3D"CP17_034_01"=
Triangles
Example, continu= ed
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» A triangular lot= is = 140 feet long and 50 = feet wide at its base. What is the area?
» Variation 2:= 3;
» A =3D 50 × (½ × 140)
»    A =3D 50 × 70
»    A =3D 3,500 sq. feet
<= ![if !vml]>3D"CP17_034_01"=
Triangles
Example, continu= ed
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» A triangular lot= is = 140 feet long and 50 = feet wide at its base. What is the area?
» Variation 3:= 3;
» A =3D (50 × 140= ) ÷ 2
»    A =3D 7,000 ÷ 2
»    A =3D 3,500 sq. feet
<= ![if !vml]>3D"CP17_034_01"=
Triangles
Example, continu= ed
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Area Problems
Odd shapes
»To find the area of an irregular shape:
1.Divide the figure up into squares, rectangles, and right triangles.
------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0194.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
Area Problems
Odd shapes
»To find the area of an irregular shape:
1.Divide the figure up into squares, rectangles, and right triangles.= 3;
2.Find the a= rea of each of the shapes
that make up the figure.
<= span style=3D'visibility:hidden'>»
------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0195.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
Area Problems
Odd shapes
»To find the area of an irregular shape:
1.Divide the figure up into squares, rectangles, and right triangles.= 3;
2.Find the a= rea of each of the shapes
that make up the figure.
<= span style=3D'mso-special-format:"numbullet3\,1";color:#CCCCFF;mso-color-index:= 6; position:absolute;left:-7.57%;top:.16em;font-size:85%'>3.Add the ar= eas together.
<= span style=3D'visibility:hidden'>»
------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0020.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
» The lot’s western side is 60 feet long. Its = northern side is 100 feet long, but its southern side is 1= 20 feet long.
» To find the area of this lot, break it into a rectangle and a triangle.
<= ![if !vml]>=3Df20
Odd Shapes
Example
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------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0023.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
»To find the length of t= he = triangle’s base, subtract length of northern boundary from leng= th of southern boundary.
»120 – 1= 00 =3D 20 feet
»Area of triangle:
»A =3D (½ × 20) × 60 = ;
»A =3D 600 sq. feet
<= ![if !vml]>
Odd Shapes
Example, continu= ed
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»Total area:
» 6,000 + 600 =3D
6,600 sq. feet =
<= ![if !vml]>=3Df24
Odd Shapes
Example, continu= ed
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»A common mist= ake = when working with odd shapes is to calculate the area of part of the figure = twice. This can happen with a figure like this one.
<= ![if !vml]>3D"CP17_042_01"
Odd Shapes
Avoid counting s= ame section twice
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» Here’s the wrong way to calculate the area of this lot.
» 25 × 50 =3D 1,250
» 40 × 20 =3D 800
» 1,250 + 800 =3D 2,050
» By doing it this way, you measure the middle of the shape twice.
<= ![if !vml]>3D"CP17_045_01"=
Odd Shapes
Avoid counting s= ame section twice
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»<= /span>Avoid the problem by breaking the shape down like this instead.
»
»<= /span>Find height of smaller rectangle by subtracting = height of top rectangle (25 feet) from height of = the whole shape (40 feet).
<= ![if !vml]>3D"CP17_043_01"
Odd Shapes
Avoid counting s= ame section twice
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»Avoid the problem by breaking the shape d= own like this instead.
»
»Find height of smaller rectangle by subtracting height of top rectangle (= 25 feet) from height of the whole shape (40 = feet).
—4= 0 – 25 =3D 15 feet
<= ![if !vml]>3D"CP17_043_01"
Odd Shapes
Avoid counting s= ame section twice
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= »Now calculate
the area of each
rectangle and add
them together:
<= ![if !vml]>3D"CP17_043_01"
Odd Shapes
Avoid counting s= ame section twice
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»Now calculate
the area of each
rectangle and add
them together:
»25 × 50= =3D 1,250 sq. ft.
»20 × 15= =3D 300 sq. ft.
»1,250 += 300 =3D 1,550 sq. ft.
<= ![if !vml]>3D"CP17_043_01"
Odd Shapes
Avoid counting s= ame section twice
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»Here’s another way to break the odd shape= = down into rectangles correctly.
<= ![if !vml]>3D"CP17_044_01"=
Odd Shapes
Avoid counting s= ame section twice
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------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0199.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
»<= /span>Here’s another way to break the odd shape down into rectangl= es c= orrectly.
»To find width of the rectangle on the right, = subtract width of left rectangle from width of = whole shape:
» 50 – 20 =3D 30 feet
<= ![if !vml]>3D"CP17_044_01"=
Odd Shapes
Avoid counting s= ame section twice
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»Now calculate
the area of each
rectangle and add
them together:
<= ![if !vml]>3D"CP17_044_01"=
Odd Shapes
Avoid counting s= ame section twice
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»Now calculate
the area of each
rectangle and add
them together:
»40 × 20= =3D 800 sq. ft.
»30 × 25= =3D 750 sq. ft.
»800 + 7= 50 =3D 1,550 sq. ft.
<= ![if !vml]>3D"CP17_044_01"=
Odd Shapes
Avoid counting s= ame section twice
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Odd Shapes
Narrative proble= ms
»Some area problems are expressed only in = narrative form, without a visual.
------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0201.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
Odd Shapes
Narrative proble= ms
»<= /span>Some area problems are expressed only in narrative form, without a visual.
»
»<= /span>In that case, draw the shape yourself and then break the shape down into rectangles and triangles.
------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0032.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
»A lot’s boundary begins
at a certain point and = runs due south for 319 = feet, then east for 426 = feet, then north for 47 feet, and then back to = the point of beginning.
Odd Shapes
Example
------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0202.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
= »A lot’s boundary begins
at a certain point and = runs due south for 319 = feet, then east for 426 = feet, then north for 47 feet, and then back to = the point of beginning.
<= span style=3D'font-size:107%;visibility:hidden'>»=
= » To solve this problem,   
   first draw the shape.
Odd Shapes
Example
------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0155.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
= »A lot’s boundary begins
at a certain point and = runs due south for 319 = feet, then east for 426 = feet, then north for 47 feet, and then back to = the point of beginning.
<= span style=3D'font-size:107%;visibility:hidden'>»=
»
Odd Shapes
Example
<= ![if !vml]>3D"CP17_047_01"
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»Break it down into a = rectangle and a triangle as shown.
»Subtract 47 from 319
to find the height of the = triangular portion.
»319 – 47 =3D 272 feet
<= ![if !vml]>3D"CP17_049_02"
Odd Shapes
Example, continu= ed
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charset="windows-1252" Principles of California Real Estate
= »Calculate the area of the rectangle.
»426 × 47 =3D
20,022 sq. ft.
<= ![if !vml]>3D"CP17_049_01"
Odd Shapes
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<= span style=3D'mso-special-format:nobullet;display:none;color:#CCCCFF;mso-color-= index: 6;font-family:"Wingdings 2";font-size:85%'>»Add together the area of the rectangle and the triang= le to find the lot’s total = square footage.
»20,022 + 57,936 =3D 77,958 sq. feet
<= ![if !vml]>3D"CP17_050_01"
Odd Shapes
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Volume Problems
»Area: A measurement of
a two-dimensional space.
------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0203.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
Volume Problems
= »<= /span>Area: A measurement of
a two-dimensional space.
»Volume: A measurement of
a three-dimensional space.
—Width, length, and height
—Cubic feet instead of square feet =
------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0038.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
Volume Problems
For= mula: V =3D L × W × H
»To calculate volume, use this formula:
»V =3D L × W × H
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Volume Problems
For= mula: V =3D L × W × H
»To calculate volume, use this formula:
»V =3D L × W × H
»Volume =3D Length × Width × Height
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Volume Problems
Cub= ic yards
»If you see a problem that asks for cubic yards, remember that there are 27 cubic feet in a cubic yard:
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Volume Problems
Cub= ic yards
»<= /span>If you see a problem that asks for cubic yards, remember that there= are 27 cubic feet in a cubic yard:
»3 feet × 3 feet × 3 fee= t =3D 27 cubic feet
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Volume Problems
Exa= mple
»= A trailer is 40 feet long, 9= feet wide, and
7 feet high. How many cubic yards does it = contain?
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Volume Problems
Exa= mple
» A trailer is 40 feet long, 9 feet wide, and
7 feet high. How many cubic yards does it = contain?
»40 × 9 × 7 =3D 2,520 cu= bic feet
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Volume Problems
Exa= mple
» A trailer is 40 feet long, 9 feet wide, and
7 feet high. How many cubic yards does it = contain?
»40 × 9 × 7 =3D 2,520 cu= bic feet
»2,520 ÷ 27 =3D 93.33 cu= bic yards
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Summary
Area and Volume
»Area of a squa= re or rectangle: A =3D L × W
»Area of a right triangle: A =3D ½ B × H
»Divide odd shapes into squares, rectangles, and triangles
»Volume: V =3D = L × W × H
»Square feet, square yards, cubic feet,
cubic yards
»
»
»
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1nfd1nn9133d1Q1i1YcdAIr92EAPICQUQ9mT3dibfdmdndmlPdqpHdqt/dmxfdqvXdubPUtCwtsB ANzFvdvJ/dvLPdzPfdzNfd3Rnd2/mM+9OiAAADs= ------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0041.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
Percenta= ge Problems
»<= /span>Many math problems ask you to find a certain percentage of another number.
This means that you will need to multiply
the percentage by that other number.
»
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Percentage Problems
Wor= king with percentages
»Percentage problems usually require you to <= span style=3D'position:absolute;top:31.5%;left:7.3%;width:97.56%;height:6.75%'>= change percentages into decimals and/or decimals into percentages.<= /span>
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Percentage Problems
Wor= king with percentages
»<= /span>Percentage problems usually require you to change percentages into decimals and/or decimals into percentages.
»
»Example: What is 85% of $150,000?
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Percentage Problems
Wor= king with percentages
»<= /span>Percentage problems usually require you to change percentages into decimals and/or decimals into percentages.
»
»Example: What is 85% of $150,000?
»    .85 × $150,000 =3D $127,500
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Percentage Problems
Exa= mple
»One common example of a percentage = problem is calculating a commission.
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Percentage Problems
Exa= mple
»<= /span>One common example of a percentage problem is calculating a commission.
»
»<= /span>Example: A home sells for $300,000. The listing broker is paid a 6% commission on the sales price. The salesperson is entitled to 60% of that commission. How much is the salesperson’s share?
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Percentage Problems
Exa= mple
»<= /span>One common example of a percentage problem is calculating a commission.
»
»<= /span>Example: A home sells for $300,000. The listing broker is paid a 6% commission on the sales price. The salesperson is entitled to 60% of that commission. How much is the salesperson’s share? <= /span>
» $300,000 × .06 =3D $18,000
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Percentage Problems
Exa= mple
»One common example of a percentage = problem is calculating a commission.
<= span style=3D'visibility:hidden'>»
»Example: A home sells for $300,000. The listing broker is paid a 6% commission on the sales price. The salesperso= n is entitled to 60% of that commission. How much is the = salesperson’s share?
»= $300,000 × .06 =3D $18,000&#= 13;
»= $18,000 × .60 =3D $10,800
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Percentage Problems
For= mula: W × % =3D P
»<= /span>Basic formula for solving percentage problems:
»Whole × Percentage =3D = Part
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Percentage Problems
For= mula: W × % =3D P
»<= /span>Basic formula for solving percentage problems:
»Whole × Percentage =3D Part
»W × % =3D P
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»The “whole” is the larger figure, such as the <= span style=3D'font-size:94%'>property’s sale price.
Percentage Problems
For= mula: W × % =3D P
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»The “whole” is= the larger figure, such as the property’s sale price.
»The “part” is the smaller figure, such as the = commission owed.
Percentage Problems
For= mula: W × % =3D P
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<= span style=3D'font-size:94%'>»The “whole” is= the larger figure, such as the property’s sale price.
»The “part” is the smaller figure, such as the = commission owed.
»Depending on the problem, the “percentage” = <= span style=3D'font-size:94%'>may be referred to as the “rate.”
—Examples: a 7% commission rate,
a 5% interest rate= , a 10% rate of return
Percentage Problems
For= mula: W × % =3D P
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»Note that you’ll also use the percentage = formula when you’re asked to calculate interest or profit.<= /div>
Percentage Problems
Int= erest and profit problems
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»Note that you’ll also use the percentage formula when you’re asked to calculate interest or profit.
»
»<= /span>Example: A lender makes an interest-only loan of $140,000. The interest rate is 6.5%. How much is the annual interest?
Percentage Problems
Int= erest and profit problems
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»Note that you’ll also use the percentage formula when you’re asked to calculate interest or profit.
»
»<= /span>Example: A lender makes an interest-only loan of $140,000. The interest rate is 6.5%. How much is the annual interest? =
»= W × % =3D P
Percentage Problems
Int= erest and profit problems
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»Note that you’ll also use the percentage formula when you’re asked to calculate interest or profit.
<= span style=3D'visibility:hidden'>»
»Example: A lender makes an interest-only loan of $140,000. The interest rate is 6.5%. How much is the annual interest?
»= W × % =3D P
»= $140,000 × .065 =3D $9,100
Percentage Problems
Int= erest and profit problems
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»Example: An investor makes an $85,000 = investment. She receives a 12% annual return = on her investment. What is the amount of her <= span style=3D'font-size:94%'>profit?
Percentage Problems
Int= erest and profit problems
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»Example: An in= vestor makes an $85,000 investm= ent. She receives a 12% annual return on her investment. What is the amount of her <= span style=3D'font-size:94%'>profit?
» W × % =3D P
»= $85,000 × .12 =3D $10,200
Percentage Problems
Int= erest and profit problems
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»<= /span>If you need to determine the percentage (the rate) or the amount of the whole, rearrange the formula to isolate the unknown on one side of the equals sign.
»= A =3D B × C P =3D W × %
Percentage Problems
Iso= lating the unknown
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»<= /span>If you need to determine the percentage (the rate) or the amount of the whole, rearrange the formula to isolate the unknown on one side of the equals sign.
»= A =3D B × C P =3D W × %
»= A ÷ B =3D C P ÷ W =3D %
Percentage Problems
Iso= lating the unknown
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»<= /span>If you need to determine the percentage (the rate) or the amount of the whole, rearrange the formula to isolate the unknown on one side of the equals sign.
»= A =3D B × C P =3D W × %
»= A ÷ B =3D C P ÷ W =3D %
»= A ÷ C =3D B P ÷ % =3D W
Percentage Problems
Iso= lating the unknown
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»Example: An investor makes an $85,000 = investment and receives a $10,200 return. What = is the rate of return?
Percentage Problems
Fin= ding the percentage or rate
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»Example: An in= vestor makes an $85,000 investm= ent and receives a $10,200 return. What is the rate of return?
»P ÷ W =3D %
»$10,200 ÷ $85,000 =3D .12 (or 12%)
Percentage Problems
Fin= ding the percentage or rate
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»Example: An investor receives a $10,200 return = on her investment. This is a 12% return on her = investment. How much did she invest?
Percentage Problems
Fin= ding the whole
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»Example: An in= vestor receives a $10,200 return on her investment. This is a 12% return on her = investment. How much did she invest?
»P ÷ % =3D W
»= $10,200 ÷ .12 =3D $85,000
Percentage Problems
Fin= ding the whole
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Percentage Problems
Multiply or divid= e?
»= Knowing when to divide or to multiply can
be the hardest part of solving percentage = problems. Rule of thumb:
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Percentage Problems
Multiply or divid= e?
» Knowing when to divide or to multiply can
be the hardest part of solving percentage = problems. Rule of thumb:
—If= the missing element is the part (the smaller number), it’s a multiplication problem.
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Percentage Problems
Multiply or divid= e?
»= Knowing when to divide or to multiply can
be the hardest part of solving percentage = problems. Rule of thumb:
—If= the missing element is the part (the smaller number), it’s a multiplication problem.
—If = the missing element is either the whole (the larger number) or t= he percentage, it’s a division problem.
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»Example: A lender makes an interest-only loan <= span style=3D'font-size:94%'>of $140,000. The annual interest is $9,100. = What is the interest rate?
Multiply or Divide?
Finding the perc= entage or rate
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»Example: A len= der makes an interest-only loan of $140,000. The annual interest is $9,100. What is the interest rate?
»You know the p= art (the interest) and the whole (the loan amount). The percentage (the interest = rate) is the missing element, so this is a divisio= n = problem.
Multiply or Divide?
Finding the perc= entage or rate
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»Example: A len= der makes an interest-only loan of $140,000. The annual interest is $9,100. What is the interest rate?
»You know the p= art (the interest) and the whole (the loan amount). The percentage (the interest = rate) is the missing element, so this is a divisio= n = problem.
»= P ÷ W =3D %
Multiply or Divide?
Finding the perc= entage or rate
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»Example: An investor receives a $10,200 return = on her investment. This is a 12% return on her = investment. How much did she invest?=
Multiply or Divide?
Finding the whole=
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»Example: An in= vestor receives a $10,200 return on her investment. This is a 12% return on her = investment. How much did she invest?
»You know the p= art (the profit) and the percent= age (the rate of return). The whole (the total investment) is the missing element, so this = is a division problem.
Multiply or Divide?
Finding the whole=
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»Example: An in= vestor receives a $10,200 return on her investment. This is a 12% return on her = investment. How much did she invest?
»You know the p= art (the profit) and the percent= age (the rate of return). The whole (the total investment) is the missing element, so this = is a division problem.
»= P ÷ % =3D W
Multiply or Divide?
Finding the whole=
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»Example: A home sells for $300,000. The listing <= span style=3D'font-size:94%'>broker is paid a 6% commission on the sales price. The salesperson is entitled to 60% of that = <= span style=3D'font-size:94%'>commission. How much is the salesperson’s <= /span><= span style=3D'font-size:94%'>share?
Multiply or Divide?
Finding the part<= /span>
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»Example: A home sells for $300,000. The listing = broker is paid a 6% commission on the sales price. The salesperson is entitled to 60% of that = = commission. How much is the salesperson’s <= /span>= share?
»You know the whole (the sale price) and the rate. The part (the commission) is the missing = element, so this is a multiplication problem.
Multiply or Divide?
Finding the part<= /span>
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»Example: A home sells for $300,000. The listing broker is paid a 6% commission on the sales price. The salesperson is entitled to 60% of that <= span style=3D'font-size:94%'>commission. How much is the salesperson’s <= /span><= span style=3D'font-size:94%'>share?
»You know the whole (the sale price) and the rate. The part (the commission) is the missing <= span style=3D'font-size:94%'>element, so this is a multiplication problem. =
»W × % =3D P
Multiply or Divide?
Finding the part<= /span>
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Summary
Percentage Proble= ms
» Percentage formula:
»Whole × Percentage (R= ate) =3D Part
»W × % =3D P
»P ÷ W =3D %
»P ÷ % =3D W
» Types of percentage problems: commission
   problems, interest problems, and prof= it
   problems.
»
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1nfd1nn9133d1Q1i1YcdAIr92EAPICQUQ9mT3dibfdmdndmlPdqpHdqt/dmxfdqvXdubPUtCwtsB ANzFvdvJ/dvLPdzPfdzNfd3Rnd2/mM+9OiAAADs= ------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0055.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
Loan Problems
Int= erest
»You’ve already learned how to solve interest = problems where the interest is given as an annual figure.
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Loan Problems
Int= erest
»<= /span>You’ve already learned how to solve interest problems where the interest= is given as an annual figure.
»Let’s look at how to solve problems where = interest is given in semiannual, quarterly,
or monthly installments.
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Loan Problems
Int= erest
»<= /span>You’ve already learned how to solve interest problems where the interest= is given as an annual figure.
»Let’s look at how to solve problems where = interest is given in semiannual, quarterly,
or monthly installments.
—In each case, the first step is to convert
the interest into an annual figure.
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Loan Problems
Semiannual inter= est
»Example: A real estate loan calls for semiannual <= /span>= interest-only payments of $3,250. The interest = rate is 9%. What is the loan amount?=
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Loan Problems
Semiannual inter= est
»Example: A real estate loan calls for semiannual interest-only payments of $3,250. The interest rate is 9%. What is the loan amount?
» Semiannual: two payments per year.
»$3,250 × 2 =3D $6,500 annual interest
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Loan Problems
Semiannual inter= est
»Example: A real estate loan calls for semiannual interest-only payments of $3,250. The interest rate is 9%. What is the loan amount? =
» Semiannual: two payments per year.
»$3,250 × 2 =3D $6,500 annual interest
» You know the part (the interest) and the rate.
You need to find the whole (the= loan amount).
»P ÷ % =3D W.
» $6,500 ÷ .09 =3D $72,222.22
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Loan Problems
Qua= rterly interest
»<= /span>Example: A real estate loan calls for quarterly = interest-only payments of $2,371.88. The loan balance is $115,000. What is the interest rate?
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Loan Problems
Qua= rterly interest
»Example: A real estate loan calls for quarterly interest-only payments of $2,371.88. The loan balance is $115,000. What is the interest rate?
» Quarterly: 4 payments per year.
»$2,371.88 × 4 =3D $9,= 487.52 (annual interest)
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Loan Problems
Qua= rterly interest
»Example: A real estate loan calls for quarterly interest-only payments of $2,371.88. The loan balance is $115,000. What is the interest rate?
» Quarterly: 4 payments per year.
»$2,371.88 × 4 =3D $9,= 487.52 (annual interest)
» You know the part (the interest) and the whole
(the loan amount). You need to = find the rate.
»P ÷ W =3D %.
»$9,487.52 ÷ $115,000 =3D .0825, or 8.25%
»
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Loan Problems
Mon= thly interest
»Example: The interest portion of a loan’s monthly = payment is $517.50. The loan balance is $92,000. <= /span>What is the interest rate?
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Loan Problems
Mon= thly interest
»Example: The interest portion of a loan’s monthly payment is $517.50. The loan balance is $92,000. What is the interest rate?
» Monthly: 12 payme= nts per year
»$517.50 × 12 =3D $6,210 (annual interest)
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Loan Problems
Mon= thly interest
»Example: The interest portion of a loan’s monthly payment is $517.50. The loan balance is $92,000. What is the interest rate?
» Monthly: 12 payme= nts per year
»$517.50 × 12 =3D $6,210 (annual interest)
» You know the part (the interest) and the whole
(the loan amount).= You need to find the rate.
»P ÷ W =3D %.
»$6,210 ÷ $92,000 =3D .0675, or 6.75%
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Loan Problems
Amortization
»Some problems will tell you the interest portion of a monthly payment and ask you to determine the loan’s curr= ent principal balance.
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Loan Problems
Amortization
»<= /span>Some problems will tell you the interest portion of a monthly paym= ent and ask you to determine the loan’s current principal balance.
»
»<= /span>Solve these in the same way as the problems just discussed.
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»Example: The interest portion of a loan’s monthly = = payment is $256.67. The interest rate is 7%. What = = is the loan balance prior to the fifth payment?
Loan Problems
Amortization
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»Example: The interest portion of a loan’s monthly payment is $256.67. The interest rate is 7%. What = is the loan balance prior to the fifth payment?= 3;
»$256.67 × 12 =3D $3,080.04 (annual interest)
Loan Problems
Amortization
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»Example: The interest portion of a loan’s monthly payment is $256.67. The interest rate is 7%. What = is the loan balance prior to the fifth payment?= 3;
»$256.67 × 12 =3D $3,080.04 (annual interest) <= /span>
» You know the part (the interest) and the rate, and <= span style=3D'font-size:88%'>you need to find the whole (the loan amount). =
»P ÷ % =3D W
»$3,080 ÷ .07 =3D $44,000
»
Loan Problems
Amortization
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»<= /span>Some problems may tell you the monthly principal and interest paym= ent (instead
of just the interest portion of the monthly payment).
»
»These require several additional steps.
Loan Problems
Amortization
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»Example: The b= alance of a loan is $96,000. The interest rate is 8%. The monthly principal and interest payment for a loan is $704.41. How much <= /span><= span style=3D'font-size:88%'>will this payment reduce the loan balance?
»
Loan Problems
Amortization
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»Loan balance: = $96,000       Monthly P&I: $704.41
»Interest rate: 8%
»&= #13;
»<= /span>Step 1: Calculate the annual interest. =
»W × % =3D P
»$96,000 × .08 =3D $7,680 (annual interest)
Loan Problems
Amortization
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»Loan balance: = $96,000       Monthly P&I: $704.41
»Interest rate: 8%
»&= #13;
»<= /span>Step 1: Calculate the annual interest. =
»W × % =3D P
»$96,000 × .08 =3D $7,680 (annual interest)
»&= #13;
»<= /span>Step 2: Calculate the monthly interest.
»$7,680 ÷ 12 =3D $640
Loan Problems
Amortization
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»Loan balance:<= /span> $96,000       Monthly P&I: $704.41
»Interest rate:= 8% <= /span>      Monthly interest: $640
»&= #13;
»Step 3: Subtra= ct monthly interest from total monthly payment to determine monthly principal.
»$704.41 – $640 =3D $64.41
Loan Problems
Amortization
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»Loan balance: $96,000       Monthly P&I: $704.41
»Interest rate: 8%       Monthly interest: $640
<= span style=3D'font-size:88%;visibility:hidden'>»
»Step 3: Subtract monthly interest from total month= ly <= span style=3D'font-size:88%'>payment to determine monthly principal.
»$704.41 – $640 =3D $64.41
<= span style=3D'font-size:88%;visibility:hidden'>»
»Step 4: Subtract monthly principal from loan = balance.
»$96,000 – $64.41 =3D $95,935.59
Loan Problems
Amortization
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»<= /span>You might see a question like this where you’re asked how much the second or third payment will reduce the loan balance.
Loan Problems
Amortization
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»You might see a question like this where you’re asked how much the second or third payment will reduce the loan balance.
»
»<= /span>In that case, you would calculate the first payment’s effect and then repeat the four steps again, using the new balance.
Loan Problems
Amortization
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»Step 1:   $95,935.59 × .08 =3D $7,674.85
»Step 2:   $7,674.85 ÷ 12 =3D $639.57
»Step 3:   $704.41 – $639.57 =3D $64.84
»Step 4:   $95,935.59 – $64.84 =3D $95,870.75
Loan Problems
Amortization
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»Step 1:   $95,935.59 × .08 =3D $7,674.85
»Step 2:   $7,674.85 ÷ 12 =3D $639.57
»Step 3:   $704.41 – $639.57 =3D $64.84
»Step 4:   $95,935.59 – $64.84 =3D $95,870.75= 3;
»The second payment would reduce the loan <= span style=3D'font-size:88%'>balance to $95,870.75.
Loan Problems
Amortization
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»Step 1:   $95,935.59 × .08 =3D $7,674.85
»Step 2:   $7,674.85 ÷ 12 =3D $639.57
»Step 3:   $704.41 – $639.57 =3D $64.84
»Step 4:   $95,935.59 – $64.84 =3D $95,870.75
»The second payment would reduce the loan <= span style=3D'font-size:88%'>balance to $95,870.75.
»To see how much the third payment would reduce <= span style=3D'font-size:88%'>the loan balance, you’d repeat the four steps yet = <= span style=3D'font-size:88%'>again.
Loan Problems
Amortization
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Summary
Loan Problems
» Use the percentage formula for loan problems.
»Whole × Percentage (R= ate) =3D Part
» Convert semiannual, quarterly, or monthly
   interest into annual interest before substituting
   numbers into formula.
»<= /span> Amortizat= ion problems ask you to find a loan’s
   principal balance.
»
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dGAPEvR4eCER9mCFOIhZN0O1+fW4eU2VWPZs1/bE2YmleGOneG7RuW71Nhu3OIvd2ZX/9otn9IsJ deFmOfkSdXn7pnlnNpd3WZfb+I0FOigtNVO7L3s3tcuU8lO9d6H9+KGNGZCfdpCjdlVlEZH3L5Hh d1YDjSw9mmtrywzXEn8TrWyDFZNPepz+V33eVALX9qUNOEUT+JPJLp0XOJ/w1oHZeXi5WJVf+aeL t5XlGXBZFoNdMFz5roMf1Z8B+p/TIl0xyfCCeaqH2V3ddYUt95i1GpnvNSQ4wl9ZtQphJodxGKcI VsOYqIerWa2vua3bywyJGDi7SDj/IRYjv9liw5lOyRn3PNac/RqKz3lkDY4hSpan39mwKXiovVio GTvhvNqejTqhyFifaxmNr6JmmzqzedmNdxaOSfh6QTsTjXKPjTZoSxvlxG+rVXtev9gByuyxyTeQ 0deQg+mi2ddqFXSjF9RBHdl+GxlXJZmSfatXMDSlL/lsWRpt8xKmO9ltQ/m5/5KBS5lPcfqUdVqL fTpb4Xm7fXqeGZtbWe2xI1vICtey3cuD0ZsyNXu9B++zfdmFHpeqT3iYsZrZVvu+kRZwSwe2lflK bRh0CRSaadNLp5l+E5atsdmtq8iStQiJu5liKZZ27+3e5hR3+RpP+5rfpvumCQh4/xH7w3saqGf0 u0fcu018xFOGvwt1vPWOsiOOnzdYr57Xqdnbce7CsweaMJ7koDGVU4nSobmXoYUcoon8mFu7Rmt0 TFS8VE1rtrXSttW3fXN7kXWbmj+afr02pNUyfxfNpP33LQH4PCYNL8mck/XygGmaWUE5ujncpq07 p+Eci11Zu7t7uxWbxId6qFtjyREoJEzCzxMA0AUdAP6c0APd0Ae90BX90Bc90Rn90R090hF90hud 0g99KQYd0wFA0zn90i8dAUKC00F900e9K0K91FH91FWd1Ffd1Fn91V091lMd1mdd1lu91nH91nWd 1nfd1nn9133d1Q1i1YcdAIr92EAPICQUQ9mT3dibfdmdndmlPdqpHdqt/dmxfdqvXdubPUtCwtsB ANzFvdvJ/dvLPdzPfdzNfd3Rnd2/mM+9OiAAADs= ------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0072.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
Profit or Loss Problems
»Another common type of percentage problem involves a property owner’s profit or loss over a period of time.
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Profit or Loss Problems
»Another common type of percentage problem involves a property owner’s profit or loss over a period of time.
—He= re the “whole” is the property’s value at an earlier point (which w= e’ll call Then).
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Profit or Loss Problems
»Another common type of percentage problem involves a property owner’s profit or loss over a period of time.
—He= re the “whole” is the property’s value at an earlier point (which w= e’ll call Then).
—The “part” is the property’s value at a later point (which we’ll call N= ow).
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Profit or Loss Problems
“Then” and “Now” formula
»<= /span>The easiest way to approach these
problems is by using this modification
of the percentage formula:
»Then × Percentage =3D N= ow
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Profit or Loss Problems
“Then” and “Now” formula
»<= /span>The easiest way to approach these
problems is by using this modification
of the percentage formula:
»Then × Percentage =3D Now
»
»Of course, this= can be changed to:
»Now ÷ Percentage =3D Then
»Now ÷ Then =3D Percenta= ge
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Profit or Loss Problems
Cal= culating a loss
»Example: A seller sells her house for $220,000, = which represents a 30% loss. How much did she = originally pay for the house?
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Profit or Loss Problems
Cal= culating a loss
= »Example: A sel= ler sells her house for $220,000, which represents a 30% loss. How much did she originally pay for the house?
—You know the Now value and the percentage <= /span>of the loss.
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Profit or Loss Problems
Cal= culating a loss
= »Example: A sel= ler sells her house for $220,000, which represents a 30% loss. How much did she originally pay for the house?
—You know the Now value and the percentage <= /span>of the loss.
—You need = to find the Then value (the original value of the house).
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Profit or Loss Problems
Cal= culating a loss
= »Example: A sel= ler sells her house for $220,000, which represents a 30% loss. How much did she originally pay for the house?
—You know the Now value and the percentage <= /span>of the loss.
—You need = to find the Then value (the original value of the house).
<= span style=3D'font-size:94%'>—Rearrange the basic formula to isolate Then: <= /span>
»Now ÷ Percentage =3D Then
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Profit or Loss Problems
Cal= culating a loss
»Now ÷ Percentage =3D Then
»$220,000 ÷ .70 =3D $314,286
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Profit or Loss Problems
Cal= culating a loss
»Now ÷ Percentage =3D Then
»$220,000 ÷ .70 =3D $314,286
»The key to solving this problem is choosing the = correct percentage to put into the formula.=
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Profit or Loss Problems
Cal= culating a loss
»Now ÷ Percentage =3D Then
»$220,000 ÷ .70 =3D $314,286
»The key to solving this problem is choosing the = correct percentage to put into the formula.
<= span style=3D'font-size:94%'>—Here the correct percentage is 70%, not 30%.
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Profit or Loss Problems
Cal= culating a loss
»Now ÷ Percentage =3D Then
»$220,000 ÷ .70 =3D $314,286
»The key to solving this problem is choosing the = correct percentage to put into the formula.
<= span style=3D'font-size:94%'>—Here the correct percentage is 70%, not 30%. <= /span>
—The house didn’t sell for 30% of its original value. It sold for 30% less than its original value.
»100% – 30% =3D 70%
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Profit or Loss Problems
Cal= culating a loss
»When dealing with a loss, you can determine the <= span style=3D'font-size:94%'>rate using this formula:
» 100% – Percentage Lost =3D Percentage Received
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Profit or Loss Problems
Cal= culating a loss
»When dealing with a loss, you can determine the <= span style=3D'font-size:94%'>rate using this formula:
» 100% – Percentage Lost =3D Percentage Received
» It’s the percentage received that must be used
in the formula.
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Profit or Loss Problems
Cal= culating a gain
»To calculate a gain in value, add the percentage <= /span>= gained to 100% find the percentage received:
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Profit or Loss Problems
Cal= culating a gain
»To calculate a= gain in value, add the percentage gained to 100% find the percentage received:
= »100% + Percentage Gained =3D
Percentage Received
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Profit or Loss Problems
Cal= culating a gain
»To calculate a= gain in value, add the percentage gained to 100% find the percentage received:
= »100% + Percentage Gained =3D
Percentage Received =
»Returning to the example, if the sale had <= /span>resulted in a 30% profit instead of a 30% loss, <= span style=3D'font-size:94%'>that would mean the house sold for 130% of = <= span style=3D'font-size:94%'>what the seller originally paid for it:
»100% + 30% =3D 130%
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Profit or Loss Problems
Cal= culating a gain
»Example: A seller sells her house for $220,000, <= span style=3D'font-size:94%'>which represents a 30% loss. How much did <= /span>= she originally pay for the house?
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Profit or Loss Problems
Cal= culating a gain
»Example: A sel= ler sells her house for $220,000, which represents a 30% loss. How much did she originally pay for the house?
»$220,000 ÷ 1.30 =3D $169,231
»Now ÷ Percentage Received =3D Then
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Profit or Loss Problems
Cal= culating a gain
»Note that if a seller sells a house for 130% of <= span style=3D'font-size:94%'>what she paid for it, she didn’t make a 130% = profit.
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Profit or Loss Problems
Cal= culating a gain
»Note that if a seller sells a house for 130% of what she paid for it, she didn’t make a 130% profit.
»&= #13;
»She received 1= 00% of what she paid, plus 30%. She received a 30% profit.
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Profit or Loss Problems
App= reciation and depreciation
»A profit or loss problem may also be = expressed in terms of appreciation or depreciation.
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Profit or Loss Problems
App= reciation and depreciation
»<= /span>A profit or loss problem may also be expressed in terms of appreciation or depreciation.
»
»<= /span>If so, the problem is solved the same way as an ordinary profit and loss problem.
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Profit or Loss Problems
Com= pound depreciation
»You may see problems where you’re told
how much a property appreciated or = depreciated per year over several years.
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Profit or Loss Problems
Com= pound depreciation
»<= /span>You may see problems where you’re told
how much a property appreciated or = depreciated per year over several years.
»
»<= /span>This requires you to repeat the same calculation for each year= .
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»Example: A property is currently worth <= span style=3D'font-size:94%'>$220,000. It has depreciated four and a half percent per year for the past five years. What = was the property worth five years ago?
Profit or Loss Problems
Com= pound depreciation
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»The house is l= osing value, so first subtract the
rate of loss from 100%.
»100% – 4.5% =3D 95.5%, or .955
Profit or Loss Problems
Com= pound depreciation
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»The house is losing value, so first subtract the <= br> rate of loss from 100%.
»100% – 4.5% =3D 95.5%, or .955
»
»You know the Now value and the rate.
The missing element is the Then value:
»Now ÷ Percentage =3D Then
»$220,000 ÷ .955 =3D $230,366.49
Profit or Loss Problems
Com= pound depreciation
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»The house is l= osing value, so first subtract the
rate of loss from 100%.
»100% – 4.5% =3D 95.5%, or .955
» =
»You know the N= ow value and the rate.
The missing element is the Then value:
»Now ÷ Percentage =3D Then
»$220,000 ÷ .955 =3D $230,366.49
» The house was wor= th $230,366 one year ago.
Profit or Loss Problems
Com= pound depreciation
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» = Now repeat the calculation four more times, to determine how much the house was worth five = years ago:
»
»$230,366 ÷ .955 =3D $= 241,221 (value 2 years ago)
Profit or Loss Problems
Com= pound depreciation
------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0266.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
» = Now repeat the calculation four more times, to determine how much the house was worth five = years ago:
»
»$230,366 ÷ .955 =3D $= 241,221 (value 2 years ago)
»$241,221 ÷ .955 =3D $= 252,587 (value 3 years ago)
Profit or Loss Problems
Com= pound depreciation
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» = Now repeat the calculation four more times, to determine how much the house was worth five = years ago:
»
»$230,366 ÷ .955 =3D $= 241,221 (value 2 years ago)
»$241,221 ÷ .955 =3D $= 252,587 (value 3 years ago)
»$252,587 ÷ .955 =3D $= 264,489 (value 4 years ago)
Profit or Loss Problems
Com= pound depreciation
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» = Now repeat the calculation four more times, to determine how much the house was worth five = years ago:
»
»$230,366 ÷ .955 =3D $= 241,221 (value 2 years ago)
»$241,221 ÷ .955 =3D $= 252,587 (value 3 years ago)
»$252,587 ÷ .955 =3D $= 264,489 (value 4 years ago)
»$264,489 ÷ .955 =3D $= 276,952 (value 5 years ago)
Profit or Loss Problems
Com= pound depreciation
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»If you’re told that a property gained value at a = particular rate over several years, you’ll use the same process.
Profit or Loss Problems
Com= pound appreciation
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»If you’re told that a property gained value at a particular rate ov= er several years, you’ll use the same process.
»
»<= /span>The difference is that you’ll need to add
the rate of change to 100%, instead of subtracting it from 100%.
Profit or Loss Problems
Com= pound appreciation
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»Example: A property is currently worth <= span style=3D'font-size:94%'>$380,000. It has appreciated in value 4% per year for the last four years. What was it worth = four years ago?
Profit or Loss Problems
Com= pound appreciation
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»<= /span>Add the rate of appreciation to 100%. <= /span>
»100% + 4% =3D 104%, or 1.04
Profit or Loss Problems
Com= pound appreciation
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»<= /span>Add the rate of appreciation to 100%. <= /span>
»100% + 4% =3D 104%, or 1.04
»You know the N= ow value and the rate of change, so use the formula Now ÷ Percentage =3D Then.
Profit or Loss Problems
Com= pound appreciation
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»<= /span>Add the rate of appreciation to 100%. <= /span>
»100% + 4% =3D 104%, or 1.04
»You know the N= ow value and the rate of change, so use the formula Now ÷ Percentage =3D Then.
» $380,000 ÷ 1.04 = =3D $365,385 (value 1 year ago)
» $365,385 ÷ 1.04 =3D $351,332 (value 2 years ago)= 3;
» $351,332 ÷ 1.04 =3D $337,819 (value 3 years ago)= 3;
» $337,819 ÷ 1.04 =3D $324,826 (value 4 years ago)
Profit or Loss Problems
Com= pound appreciation
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Summary
Profit or Loss Pr= oblems
» Then × Pe= rcentage =3D Now
» To find t= he percentage received:
— If there’= s been a loss in value, subtract= the  
   rate of change from 100%. =
— If there’= s been a gain (a profit), add the
   rate of change to 100%.
»<= /span> Compound appreciation and depreciation:
   repeat the profit or loss calculation as needed.
»
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1nfd1nn9133d1Q1i1YcdAIr92EAPICQUQ9mT3dibfdmdndmlPdqpHdqt/dmxfdqvXdubPUtCwtsB ANzFvdvJ/dvLPdzPfdzNfd3Rnd2/mM+9OiAAADs= ------=_NextPart_01C8DA17.A0E0F720 Content-Location: file:///C:/B07812E8/17Math_files/slide0087.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="windows-1252" Principles of California Real Estate
Capitali= zation Problems
»= Capitalization: The process used to convert a property’s income into the property’s value.
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Capitali= zation Problems
» Capitaliza= tion: The process used to convert a property’s income into the property’s value.
—In= the appraisal of income property, the property’s value depends on its income.
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Capitali= zation Problems
» Capitaliza= tion: The process used to convert a property’s income into the property’s value.
—In= the appraisal of income property, the property’s value depends on its income.
§The value is= the price an investor would
be willing to pay for the property.
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Capitali= zation Problems
» Capitaliza= tion: The process used to convert a property’s income into the property’s value.
—In= the appraisal of income property, the property’s value depends on its income.
§The value is= the price an investor would
be willing to pay for the property.
§The property= ’s annual net income is the return on the investment.
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Capitalization Problems
For= mula: V × % =3D I
»Capitalization problems are another type of = percentage problem.
»= Whole × Percentage =3D Part
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Capitalization Problems
For= mula: V × % =3D I
»Capitalization problems are another type of = percentage problem.
»= Whole × Percentage =3D Part
»Here the “part” is the property’s income, and the “whole” is the property’s value:
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Capitalization Problems
For= mula: V × % =3D I
»Capitalization problems are another type of = percentage problem.
»= Whole × Percentage =3D Part
»Here the “part” is the property’s income, and the “whole” is the property’s value:
»= Value × Capitalization Rate =3D Income
»= or
»= Income ÷ Rate =3D Value
»= or
»= Income ÷ Value =3D Rate
»
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Capitalization Problems
Capitalization r= ate
»The capitalization rate represents the rate of return an investor would be likely to want on this investment.
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Capitalization Problems
Capitalization r= ate
»<= /span>The capitalization rate represents the rate of return an investor would be likely to want on this investment.
»An investor who wants a higher rate of
return would not be willing to pay as much
for the property as an investor who’s willing = to accept a lower rate of return.
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Capitalization Problems
Cal= culating value
»Example: A property generates an annual net <= span style=3D'font-size:94%'>income of $48,000. An investor wants a 12% = <= span style=3D'font-size:94%'>rate of return on his investment. How much = <= span style=3D'font-size:94%'>could he pay for the property and realize his <= span style=3D'font-size:94%'>desired rate of return?
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Capitalization Problems
Cal= culating value
»Example: A pro= perty generates an annual net income of $48,000. An investor wants a 12% rate of return on his investment. How much could he pay for the property and realize his <= span style=3D'font-size:94%'>desired rate of return?
»Income ÷ Rate =3D Value
»$48,000 ÷ .12 =3D $400,000
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Capitalization Problems
Cal= culating value
»Example: A pro= perty generates an annual net income of $48,000. An investor wants a 12% rate of return on his investment. How much could he pay for the property and realize his <= span style=3D'font-size:94%'>desired rate of return?
»Income ÷ Rate =3D Value
»$48,000 ÷ .12 =3D $400,000
»   The inv= estor could pay $400,000 for this property and realize a 12% return.
»
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»Example: An investment property has a net <= /span>= income of $40,375. An investor wants a 10.5% = rate of return. What would the value of the <= span style=3D'font-size:94%'>property be for her?
Capitalization Problems
Calculating value=
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»Example: An investment property has a net income of $40,375. An investor wants a 10.5% rate of return. What would the value of the <= span style=3D'font-size:94%'>property be for her?
»Income ÷ Rate =3D Value
»$40,375 ÷ .105 =3D $384,524
»= She could pay $384,524 for t= his property