FORMULAS

Three-Variable Formulas

In three-variable formulas, each variable is a function of the other two.

Income Formula Property Tax Formula
Income = Rate x Value Tax = Assessed Value x Rate
I = R x V R = I ÷ V V = I ÷ R T = A x R A = T ÷ R R = T ÷ A
Percentage Formula Percentage = Rate x Base P = R x B R = P ÷ B B = P ÷ R Commission Formula Commission = Sale Price x Rate C = S x R S = C ÷ R R = C ÷ S

Area Formula

Area = Length x Width

A = L x W

L = A ÷ W

W = A ÷ L

INTEREST COMPUTATION AND TABLES

Simple interest computation involves multiplying the principal (amount of note) by the selected interest rate and
the product or result is the interest for one year. Remember, the interest rate (.06 or .09 for example) is a
decimal and two points are to be marked off from the right.

There are 12 months in a year or 365 days. This latter figure makes for an awkward denominator. As a result, as
an acceptable business practice, we assume 12 months of 30 days each, and 360 days to a year.

To avoid long computations which may involve cumbersome fractions, it is common to use prepared
computations in the form of interest tables which show the base as $1, $100 or $1,000 for a variety of interest
and time periods. From the interest table, we determine the factor and multiply it by the amount involved if it
exceeds or is less than the base of the table. The following illustrates the different methods and short cuts.

Long Conventional Method

1. What is the interest on $4,650 for 75 days at 10 percent?

2. What is the interest on $4,650 for 1 year, 4 months and 10 days at 10 percent?

Answer:

1. 4650 x .10 x 75/360 = $96.88

2. 4650 x .10 x {360 + 120 + 10} or 490/360 = $632.92

(proper fraction for periods if less than 1 year; improper fraction for periods of more than 1 year)

Use of Interest Tables Method

1. Same problem

Look in table on next page for 30 days at 10 percent

factor is 8.3340 = 30

factor is 8.3340 = 30

factor for 15 days 4.1670 = 15

20.8350 75 days

$4,650 = $4.65 per $1,000

Multiply $4.65 x 20.8350 = $96.88

2. Table not complete to show higher factors, but it could be done this way:

30 day factor 8.3340

x 16 (16 months)

133.3440

2.7780 (10 days)

136.1220 factor for 1 year,

4 months and 10 days at $1,000

Therefore, 136.1220 x 4.65 (number of thousands) = $632.92 interest.

INTEREST TABLE FIGURED ON $1,000

360 Days to the Year

Days 5% 6% 7% 8% 9% 10%
1 $0.1389 $0.1667 $0.1944 $0.2222 $0.2500 $0.2778
2 0.2778 0.3333 0.3889 0.4444 0.5000 0.5556
3 0.4167 0.5000 0.5833 0.6666 0.7500 0.8334
4 0.5556 0.6667 0.7778 0.8888 1.0000 1.1112
5 0.6944 0.8333 0.9722 1.1111 1.2500 1.3890
6 0.8333 1.0000 1.1667 1.3333 1.5000 1.6668
7 0.9722 1.1667 1.3611 1.5555 1.7500 1.9446
8 1.1111 1.3333 1.5556 1.7777 2.0000 2.2224
9 1.2500 1.5000 1.7500 2.0000 2.2500 2.5002
10 1.3889 1.6667 1.9444 2.2222 2.5000 2.7780
11 1.5278 1.8333 2.1389 2.4444 2.7500 3.0558
12 1.6667 2.0000 2.3333 2.6666 3.0000 3.3336
13 1.8056 2.1667 2.5278 2.8888 3.2500 3.6114
14 1.9444 2.3333 2.7222 3.1111 3.5000 3.8892
15 2.0833 2.5000 2.9167 3.3333 3.7500 4.1670
16 2.2222 2.6667 3.1111 3.5555 4.0000 4.4448
17 2.3611 2.8333 3.3055 3.7777 4.2500 4.7226
18 2.5000 3.0000 3.5000 4.0000 4.5000 5.0004
19 2.6389 3.1667 3.6944 4.2222 4.7500 5.2782
20 2.7778 3.3333 3.8889 4.4444 5.0000 5.5560
21 2.9167 3.5000 4.0833 4.6666 5.2500 5.8338
22 3.0556 3.6667 4.2778 4.8888 5.5000 6.1116
23 3.1944 3.8333 4.4722 5.1111 5.7500 6.3894
24 3.2222 4.0000 4.6667 5.3333 6.0000 6.6672
25 3.4722 4.1667 4.8611 5.5555 6.2500 6.9450
26 3.6111 4.3333 5.0555 5.7777 6.5000 7.2228
27 3.7500 4.5000 5.2500 6.0000 6.7500 7.5006
28 3.8889 4.6667 5.4444 6.2222 7.0000 7.7784
29 4.0278 4.8333 5.6389 6.4444 7.2500 8.0562
30 4.1667 5.0000 5.8333 6.6666 7.5000 8.3340

LINEAR AND SPATIAL MEASUREMENTS AS USED IN APPRAISING AND LAND DESCRIPTIONS

Common Linear Measurements

One foot = 12 inches

One yard = 3 feet or 36 inches

One rod = 16 1/2 feet or 5 1/2 yards

One furlong = 40 rods

100 feet = 6.6 rods

One mile = 5,280 feet; 1,760 yards; 320 rods; or 80 chains

Surveyors’ Measurements

1 link = 7.92 inches

1 rod = 25 links

1 chain = 4 rods or 66 feet

(These are the old surveyors’ measurements. Modern surveyors use a steel tape or what is called an
engineer’s chain which is 100 feet long with links of one foot. Thus, a mile measured by a modern steel tape
chain is 52.8 chains.)

Spatial or Area Measurements (Length x Width)

1 square foot = 144 square inches

1 square yard = 9 square feet

1 square rod = 30 1/4 square yards

1 acre = 10 square chains; 160 square rods; 4,840 square yards; 43,560 square feet

(An acre is an odd and inconsistent measurement. It is supposed to have been the amount of land that a
farmer could plow in a day with oxen and the old wooden plow. As a square, it is approximately 208.71 feet
on a side.)

A section = 1 square mile or 640 acres

A township = 36 square miles

A quarter section = 160 acres

Area of a square or rectangle = length x width in unit of linear measurement used

Area of a triangle = base x 1/2 height

Cubic Measurement (Length x Width x Height)

1 cubic foot = 1,728 cubic inches.

1 cubic yard = 27 cubic feet.

OTHER SHORTCUT METHODS FOR COMPUTING SIMPLE INTEREST

4% Multiply the principal by number of days; cut off right-hand figure and divide by 9.

5% Multiply by number of days and divide by 72.

6% Multiply by number of days; cut off right-hand figure and divide by 6.

7% Compile the interest for 6% and add 1/6.

8% Multiply by number of days and divide by 45.

9% Multiply by number of days; cut off right-hand figure and divide by 4.

10% Multiply by number of days and divide by 36.

BANKERS 12%-30 DAY/6%-60 DAY INTEREST COMPUTATION METHOD

(Using 360 day year)

To find interest on any principal amount for 30 days at 12%, or for 60 days at 6%, simply move the decimal
point in the principal amount two places to the left.

Therefore, the interest amount on $8432.67 at 12% for 30 days is $84.33.

Likewise, the interest amount on $8432.67 at 6% for 60 days is $84.33

(Since 12% per annum is 1% a month, and 1% of any number is the hundredth part of it, then by pointing off
two places from the right of a number, it is in effect divided by 100.)

What is the interest on $7397.64 at 9% for 69 days?

Interest @ 6% for 60 days = $73.98 (move decimal two places to left)

Interest @ 3% for 60 days = 36.99 (1/2 of 6% amount)

Interest @ 9% for 60 days = 110.97

We still need 9 days more interest:

6 days = 1/10 of 60 days: 6 days = 11.09 (1/10 of $110.97)

3 days = 1/2 of 6 days 3 days = 5.55 (1/2 of $11.09)

9 days = 16.64

Therefore, interest @ 9% for 69 days = $110.97 + $16.64 = $127.61

SOME METRIC EQUIVALENTS

Lengths Areas
one foot = 0.3048 meter one square foot = 0.0929 sq. meter
one yard = 0.9144 meter one square yard = 0.836 sq. meter
one mile = 1.6093 kilometers or 1609 meters one acre = 4068.8 sq. meters
one meter = 39 inches one square mile = 259 hectares or 2.59 sq. km.
one kilometer = 3281 feet or .62 miles or 1000 meters one square meter = 10.76 sq. feet
one hectare = 2.47 acres or 10,000 sq. meters

TABLE OF MONTHLY PAYMENTS
TO AMORTIZE $1,000 LOAN
Years 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 6.5%
5 17.53 17.75 17.97 18.19 18.42 18.64 18.87 19.10 19.33 19.58
6 14.75 14.97 15.19 15.42 15.65 15.87 16.10 16.34 16.57 16.83
7 12.77 12.99 13.21 13.44 13.67 13.90 14.13 14.37 14.61 14.87
8 11.28 11.50 11.73 11.96 12.19 12.42 12.66 12.90 13.14 13.41
9 10.13 10.35 10.58 10.81 11.04 11.28 11.52 11.76 12.01 12.27
10 9.20 9.43 9.66 9.89 10.12 10.36 10.61 10.85 11.10 11.38
11 8.45 8.67 8.90 9.14 9.38 9.62 9.86 10.11 10.37 10.64
12 7.82 8.05 8.28 8.51 8.76 9.00 9.25 9.50 9.76 10.04
13 7.28 7.51 7.75 7.99 8.23 8.48 8.73 8.99 9.25 9.53
14 6.83 7.06 7.30 7.54 7.78 8.03 8.29 8.55 8.81 9.10
15 6.44 6.67 6.91 7.15 7.40 7.65 7.91 8.17 8.44 8.73
16 6.09 6.32 6.56 6.81 7.06 7.32 7.58 7.84 8.11 8.41
17 5.79 6.02 6.26 6.51 6.76 7.02 7.29 7.56 7.83 8.13
18 5.52 5.75 6.00 6.25 6.50 6.76 7.03 7.30 7.58 7.89
19 5.28 5.51 5.76 6.01 6.27 6.53 6.80 7.08 7.36 7.67
20 5.06 5.30 5.55 5.80 6.06 6.33 6.60 6.88 7.16 7.48
21 4.86 5.10 5.35 5.61 5.87 6.14 6.42 6.70 6.99 7.31
22 4.69 4.93 5.18 5.44 5.70 5.97 6.25 6.54 6.83 7.15
23 4.52 4.77 5.02 5.28 5.55 5.82 6.10 6.39 6.69 7.02
24 4.37 4.62 4.88 5.14 5.41 5.68 5.97 6.26 6.56 6.89
25 4.24 4.49 4.74 5.01 5.28 5.56 5.85 6.14 6.44 6.78
26 4.11 4.36 4.62 4.89 5.16 5.44 5.73 6.03 6.34 6.67
27 4.00 4.25 4.51 4.78 5.05 5.34 5.63 5.93 6.24 6.58
28 3.89 4.14 4.40 4.67 4.95 5.24 5.54 5.84 6.15 6.50
29 3.79 4.04 4.31 4.58 4.86 5.15 5.45 5.76 6.07 6.42
30 3.70 3.95 4.22 4.49 4.77 5.07 5.37 5.68 6.00 6.35
35 3.31 3.57 3.85 4.13 4.43 4.73 5.05 5.37 5.70 6.07
40 3.03 3.30 3.58 3.87 4.18 4.50 4.82 5.16 5.50 5.88

TABLE OF MONTHLY PAYMENTS

TO AMORTIZE $1,000 LOAN

Years 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% 10.5% 11.0% 11.5% 12.0% 12.5%
5 19.80 20.04 20.28 20.52 20.76 21.01 21.25 21.49 21.74 21.99 22.25 22.50
6 17.05 17.29 17.53 17.78 18.03 18.28 18.53 18.78 19.04 19.29 19.55 19.81
7 15.09 15.34 15.59 15.84 16.09 16.35 16.61 16.86 17.12 17.39 17.65 17.92
8 13.63 13.88 14.14 14.39 14.66 14.92 15.18 15.44 15.71 15.98 16.25 16.53
9 12.51 12.76 13.02 13.28 13.55 13.81 14.08 14.35 14.63 14.90 15.18 15.47
10 11.61 11.87 12.13 12.40 12.67 12.94 13.22 13.49 13.78 14.06 14.35 14.64
11 10.88 11.15 11.42 11.69 11.97 12.24 12.52 12.80 13.09 13.38 13.68 13.98
12 10.28 10.55 10.82 11.10 11.39 11.67 11.96 12.24 12.54 12.83 13.13 13.44
13 9.78 10.05 10.33 10.61 10.90 11.19 11.48 11.78 12.08 12.38 12.69 13.00
14 9.35 9.63 9.91 10.20 10.49 10.79 11.09 11.38 11.69 12.00 12.31 12.63
15 8.99 9.27 9.56 9.85 10.15 10.45 10.75 11.05 11.37 11.68 12.00 12.33
16 8.67 8.96 9.25 9.54 9.85 10.15 10.46 10.77 11.09 11.41 11.74 12.07
17 8.40 8.69 8.98 9.28 9.59 9.90 10.22 10.53 10.85 11.18 11.51 11.85
18 8.16 8.45 8.75 9.05 9.37 9.68 10.00 10.32 10.65 10.98 11.32 11.66
19 7.94 8.24 8.55 8.85 9.17 9.49 9.82 10.14 10.47 10.81 11.15 11.50
20 7.75 8.06 8.36 8.68 9.00 9.33 9.66 9.98 10.32 10.66 11.01 11.36
21 7.58 7.89 8.20 8.52 8.85 9.18 9.51 9.85 10.19 10.54 10.89 11.24
22 7.43 7.75 8.06 8.38 8.72 9.05 9.39 9.73 10.07 10.42 10.78 11.14
23 7.30 7.61 7.93 8.26 8.60 8.93 9.28 9.62 9.97 10.33 10.69 11.05
24 7.18 7.50 7.82 8.15 8.49 8.83 9.18 9.52 9.88 10.24 10.60 10.97
25 7.07 7.39 7.72 8.05 8.40 8.74 9.09 9.44 9.80 10.16 10.53 10.90
26 6.97 7.29 7.63 7.96 8.31 8.66 9.01 9.37 9.73 10.10 10.47 10.84
27 6.88 7.21 7.54 7.88 8.23 8.58 8.94 9.30 9.67 10.04 10.41 10.79
28 6.80 7.13 7.47 7.81 8.16 8.52 8.88 9.25 9.61 9.99 10.37 10.75
29 6.72 7.06 7.40 7.75 8.10 8.46 8.82 9.19 9.57 9.94 10.32 10.71
30 6.65 6.99 7.34 7.69 8.05 8.41 8.78 9.15 9.52 9.90 10.29 10.67
35 6.39 6.74 7.10 7.47 7.84 8.22 8.60 8.98 9.37 9.76 10.16 10.55
40 6.21 6.58 6.95 7.33 7.71 8.10 8.49 8.89 9.28 9.68 10.09 10.49