Business Mathematics Handbook For Contemporary Business Mathematics for Colleges, 13th Edition
by
James E. Deitz James L. Southam
© 2003 South-Western/Thomson Learning 2 Business Math Handbook
Contents
Electronic Calculators...... 1
Common Business and Algebraic Formulas...... 6
Conversions of Fractions, Decimals, and Percents...... 7
Metric Conversions ...... 8
Time Relationships...... 10
Monetary Tables...... 11
International Monetary Units...... 11
Compound Interest Tables ...... 12
Annual Percentage Rate Tables...... 26
Future Value Annuity Table...... 29
Present Value Annuity Table...... 30 Business Math Handbook 3
ELECTRONIC CALCULATORS
FEATURES IMPORTANT FOR BUSINESS
Most calculators used for business are quite simple to use and very similar in operation. There are basic features to look for in a calculator purchased for business. The following features are recommended:
1. Eight- to twelve-digit capacity. For business, eight or more digits are preferable.
2. Floating decimal point. This feature places the decimal point automatically, carrying out calculations from two decimal places to the maximum capacity of the calculator's display.
3. Percent key (%). This key eliminates the need to convert a percentage to a decimal before multiplying or dividing. For most calculators, this key reduces the number of steps required in percentage calculations by commanding the calculator to give a net percentage answer.
4. Memory register. This feature enables the user to store an amount and then add to it, subtract from it, recall it for review, multiply it, or divide it again and again until the register is cleared.
5. Repeat addition-subtraction. This feature provides a number that, once entered, can be automatically repeated in addition and subtraction by depressing the equals key.
6. Constant multipliers and divisors. This feature provides a number that, once entered, can be automatically repeated as a multiplier or divisor by entering the new dividend or multiplicand and depressing the equals key. The constant is usually the last number entered in division problems (divisor) and is usually the first number entered in multiplication problems (multiplier).
THE DECIMAL POINT
Many calculations have a decimal point. A decimal point is a period (.) used to separate a whole number on the left of the decimal from a less than whole number on the right of the decimal.
Example A $37.42 - the decimal separates the whole dollars (37) from the less than whole dollar (42 cents).
Decimals, which are not limited to representing dollars and cents, are a regular part of business calculations. Often decimal amounts are limited to a certain number of figures shown on the right side of a decimal. Many electronic calculators show up to eight figures on the right side of the decimal point. Frequently, these should be reduced, or "rounded," to just two figures. To round a number containing three or more figures on the right side of the decimal to two decimal places, start at the decimal and count to the right. If the third figure is 4 or less, leave the second figure as it is. If the third is 5 or greater, increase the second figure by one.
1 Example B 37.414 rounded to two decimal places is 37.41 4 Business Math Handbook
37.415 rounded to two decimal places is 37.42
82.333333 rounded to four decimal places is 82.3333
82.666666 rounded to four decimal places is 82.6667
Examples of decimals and rounding for use in this section are limited to their simplest form.
BASIC KEYS AND THEIR CAPABILITIES
The first booklet to read for instructions about a calculator is the one provided by the manufacturer. You should always read and do the sample problems in the manufacturer's instruction booklet. The following descriptions are compiled from a number of these booklets. They cover the basic key functions common to most hand-held calculators.
On-Off ...... Controls power. NOTE: The Off key usually clears the calculator, ...... including the memory.
C Clear Key ...... Clears the calculator except for the memory register. AC All Clear Key ...... Clears the calculator, including the memory register. 0-9 Numeral Keys ...... Used to enter numbers. CE Clear Entry Key ...... Used to clear numbers keyed incorrectly but not yet entered...... Does not clear total or memory Decimal Point Key ...... Puts a decimal point into a number. + Addition Key ...... Adds. Subtraction Key ...... Subtracts. Multiplication Key ...... Multiplies. Division Key ...... Divides. Equals Key ...... Orders the sum, the difference, the product, or the quotient. Change Sign Key ...... Converts a positive number to a negative number and vice ...... versa. % Percent Key ...... Orders computed answer to move decimal two places to the ...... left. Square Root Key ...... Computes the square root of the number in the display. Used ...... primarily in scientific calculations; seldom used in business.
For Memory Calculators:
M+ Memory Plus Key ..………….Adds the number in the display to the memory. NOTE: Used to add the results of regular register multiplication (the product) and division (the quotient) to the memory register.
M- Memory Minus Key.. Subtracts the number in the display from the memory.
MR Memory Recall Key.. Displays the contents of the memory register. NOTE: Does not clear the memory.
MC Memory Clear Key ... Displays the contents of the memory register and clears the memory register. Business Math Handbook 5
BASIC OPERATIONS
The following calculator operations are commonly used in business mathematics. You should work through the following illustrations. The steps shown can be used with most hand-held and small desk-top calculators. However, because of the number of different manufacturers, your calculator might not use the exact steps shown here. Note the differences and work the problems until you get the answers given. Consult your own instruction booklet when differences arise. Prior to operating the calculator, you should estimate your answer. You could enter an incorrect digit or operation. Estimation will give you a guide to accuracy.
Addition: 200 + 300 + 400 = 900 Enter C 200 + 300 + 400 = Display 0 200 200 300 500 400 900
Subtraction: 45.6 12.3 = 33.3 Enter C 45.6 12.3 = Display 0 45.6 45.6 12.3 33.3
Addition-Subtraction Chain: 3.91 + 14.21 1.03 + 2.16 10 = 9.25 Enter C 3.91 + 14.21 1.03 + 2.16 10 = Display 0 3.91 3.91 14.21 18.12 1.03 17.09 2.16 19.25 10 9.25
Multiplication: 300 5 = 1,500 Enter C 300 5 = Display 0 300 300 5 1,500
Multiplication by % Key (automatically moves decimal 2 places to the left): 300 5% (0.05) = 15 Enter C 300 5 % Display 0 300 300 5 15
Multiplication Chain: 1.23 45.6 789 = 44,253.432 Enter C 1.23 45.6 789 = Display 0 1.23 1.23 45.6 56.088 789 44,253.432
Division: 400 8 = 50 Enter C 400 8 = Display 0 400 400 8 50
Division by % Key (automatically moves decimal 2 places to the left): 400 8% (0.08) = 5,000 Enter C 400 8 % Display 0 400 400 8 5,000
Division Chain: 400 50 3 = 2.6666666 Enter C 400 50 3 Display 0 400 400 50 8 32.6666666
Division-Multiplication Chain: 123 456 789 = 212.8223683 Enter C 123 456 789 = Display 0 123 123 456 0.269736842 789 212.8223683 6 Business Math Handbook
Constant Multiplication: 250 4 = 1,000; 250 5 = 1,250; 250 6 = 1,500 Machine with constant program (in older-model calculators, the constant key might be the second number entered rather than the first): Enter C 250 4 = 5 = 6 = Display 0 250 250 4 1,000 5 1,250 6 1,500
Machine without constant program, but with memory register: Enter C MC 250 M+ 4 = MR 5 = MR 6 = Display 0 0 250 250 250 4 1,000 250 250 5 1,250 250 250 6 1,500
Constant Division: 208 26 = 8; 312 26 = 12; 624 26 = 24 Machine with constant program: Enter C 208 26 = 312 = 624 = Display 0 208 208 26 8 312 12 624 24
Machine without constant program, but with memory register: Enter C MC 26 M+ 208 MR = 312 MR = 624 MR = Display 0 0 26 26 208 208 26 8 312 312 26 12 624 624 26 24
Memory Problem-Hold and Recall Intermediate Answers: (3 5) + (6 11) + (13 20) = 341 Enter C MC 3 5 M+ 6 11 M+ 13 20 M+ MR Display 0 0 3 3 5 15 6 6 11 66 13 13 20 260 341
BUSINESS APPLICATIONS Example C Find the closing checkbook balance: Opening balance = $387.50; checks $17.20, $13.82, $17.60, and $29.40; deposit = $298.40. (Answer: Balance = $607.88)
Enter C 387.50 17.20 13.82 17.60 Display 0 387.50 387.50 17.20 370.30 13.82 356.48 17.60 338.88
29.40 + 298.40 = 29.40 309.48 298.40 607.88
Example D Find the average miles per gallon for an automobile driven 370 miles and using 20 gallons of gas. (Answer: average miles per gallon = 18.5) Enter C 370 20 = Display 0 370 370 20 18.5
Example E Total the invoice for 9 items @ $11.00, 7 items @ $14.00, and 3 items @ $15.00, plus 6% sales tax. (Answer: total invoice $256.52) Enter C MC 9 11 = M+ 7 14 = M+ 3 Display 0 0 9 9 11 99 99 7 7 14 9898 3 15 = M+ MR 0.06 = M+ MR 3 15 45 45 242 242 0.06 14.52 14.52 256.52 or, with % key: Enter MR 6 % + = Display 242 242 6 14.52 14.52 256.52 Business Math Handbook 7 or Enter C MC 9 11 M+ 7 14 M+ 3 15 M+ Display 0 0 9 9 11 99 7 7 14 98 3 3 15 45 MR 0.06 M+ MR 242 242 0.06 14.52 256.52 8 Business Math Handbook
COMMON BUSINESS AND ALGEBRAIC FORMULAS
Percent Formulas in Business
1. Simple Interest: I = P R T I= Interest R = Rate P = Principle T = Time (in years)
2. Compound Interest: I = P (I + r)n P I= Interest r Rate P = Principle n Number of compounding periods
Note: If your calculator does not have a power key, use (1 + r) as a factor n times.
When computing for time less than a year: a. If time is in months, use 12 as a base. b. If time is in days, use 360 as a base unless noted otherwise.
To use I = P R T you must know three of the four variables. Other versions of the formula are: a. R = I/PT b. P = I/RT c. T = I/PR
3. Markup based on cost: C + M = S C = Cost S = Selling Price M = Markup
4. Markdown/Discount: D = % S D = Discount amount % = Percent of discount S = Selling price
Algebraic Formulas
Formula Meaning Examples P = 2L+ 2W Perimeter = 2 length Distance around a rectangle + 2 width P = 4s Perimeter = 4 one Distance around a square. Used for determining side fencing, pool covers, banisters on a deck, etc.
A = l w Area of rectangle or Area of a floor, basement, or other surfaces for figuring square = length width painting, tiling, or wall-to-wall floor covering. A = S2Area of square = side side
V = lwh Volume = length Volume for figuring cost for a concrete patio Business Math Handbook 9
width height foundation or filling a pool. (Rectangular solid, or gallons of water)
V = R2h Volume = radius2 Volume for determining capacity of a silo, tank car, or height tin cans on a production line. (cylinder)
CONVERSIONS OF FRACTIONS, DECIMALS, AND PERCENTS
Fraction Decimal Percent
1/8 .125 12 1/2% 2/8 (1/4) .250 25.0% 3/8 .375 37 1/2% 4/8 (1/2) .500 50.0% 5/8 .625 62 1/2% 6/8 (3/4) .750 75.0% 7/8 .875 87 1/2 % 1/10 .100 10.0% 2/10 (1/5) .200 20.0% 3/10 .300 30.0% 4/10 (2/5) .400 40.0% 5/10 (1/2) .500 50.0% 6/10 (3/5) .600 60.0% 7/10 .700 70.0% 8/10 (4/5) .800 80.0% 9/10 .900 90.0% 1/6 .167 16.0 % 2/6 (1/3) .333 33 1/3% 3/6 (1/2) .500 50% 4/6 (2/3) .667 66 2/3% 5/6 .833 83 1/3% 1/16 .0625 6 1/4% 3/16 .1875 18 3/4% 5/16 .3125 31 1/4% 7/16 .4375 43 3/4% 9/16 .5625 56 1/4% 11/16 .6875 68 3/4% 13/16 .8125 81 1/4% 15/16 .9325 93 3/4%
METRIC CONVERSION TABLES 10 Business Math Handbook
Length Conversions
Metric to Traditional Traditional to Metric 1 kilometer (km) = 0.621 mile 1 inch = 2.54 centimeters (cm) 1 kilometer = 3,280.84 feet 1 foot = 0.305 meters (m) 1 hectometer (hm) = 328.084 feet 1 yard = 0.914 meters (m) 1 meter (m) = 1.094 yards 1 mile = 1.609 kilomters (km) 1 meter (m) = 3.281 feet 1 meter (m) = 39.370 inches 1 millimeter = 0.04 inches
If You Know Multiply by To Find If You Know Multiply by To Find Millimeters 0.04 Inches Inches 2 Centimeters Centimeters 0.4 Inches Feet 30 Centimeters Meters 3.3 Feet Yards 0.9 Meters Meters 1.1 Yards Miles 1.6 Kilometers Kilometers 0.6 Miles
Area Conversions
If You Know Multiply by To Find If You Know Multiply by To Find Square cm.(cm2) 0.16 Sq. inches Sq. inches 6.5 Sq. cm. (cm2) Square meters(m2) 1.2 Sq. yards Sq. feet 0.09 Sq. meters Sq. kilometers (km2) 0.4 Sq. miles Sq. yards 0.8 Sq. meters Hectares (ha) 2.5 Acres Sq. miles 2.6 Sq. kilometers Acres 0.4 Hectares
Weight Conversion
Metric to Traditional Traditional to Metric 1 metric tonne (t) = 1.102 short tons 1 grain = 0.065 gram (g) 1 metric tonne (t) = 2,204,623 pounds 1 ounce = 28.349 grams (g) 1 kilogram (kg) = 2.205 pounds 1 pound = 453.592 grams (g) 1 kilogram (kg) = 35.274 ounces 1 pound = 0.453 kilogram (kg) 1 hectogram (hg) = 3.527 ounces 1 short ton = 0.907 metric ton (t) 1 dekagram (dag) = 0.353 ounce 1 gram (g) = 0.035 ounce 1 decigram (dg) = 1.543 grains 1 centigram (cg) = 0.154 grain 1 milligram (mg) = 0.015 grain
If You Know Multiply by To Find If You Know Multiply by To Find Grams 0.035 Ounces Ounces 28 Grams Kilograms 2.2 Pounds Pounds 0.45 Kilograms Tonnes 1.1 Short tons Short tons 0.9 Tonnes (2000 lbs.) (2000 lbs) Business Math Handbook 11
Capacity/Volume Conversion
Metric to Traditional Tradtional to Metric 1 kiloliter (kL) = 264.178 gallons 1 pint = 0.473 liter (L) 1 hectoliter (hL) = 26.418 gallons 1 quart = 0.946 liter (L) 1 dekaliter (daL) = 2.642 gallons 1 gallon = 3.785 liters (L) 1 liter (L) = 2.113 pints 1 ounce = 29.573 milliliters (mL) 1 liter (L) = 1.057 quarts 1 cup = 0.237 liters (L) 1 liter (L) = 0.264 gallon 1 deciliter (dL) = 0.211 pint 1 centiliter (cL) = 0.338 ounce 1 milliliter (mL) = 0.034 ounce
If You Know Multiply by To Find If You Know Multiply by To Find Milliliters 0.03 Fluid ounces Teaspoons 5 Milliliters Liters 2.1 Pints Tablespoons 15 Milliliters Liters 1.06 Quarts Fluid ounces 30 Milliliters Liters 0.26 Gallons Cups 0.24 Liters Cubic meters 35 Cubic feet Pints 0.47 Liters Cubic meters 1.3 Cubic yards Quarts 0.95 Liters Gallons 3.8 Liters Cubic feet 0.03 Cubic meters Cubic yards 0.76 Cubic meters 12 Business Math Handbook
TIME RELATIONSHIPS
Second(s) Parts of a Minute Percent of a Minute (minutes) (Parts of an Hour) (Percent of an Hour) 1 1/60 1.67% 2 1/30 3.33% 5 1/12 8.33% 10 1/6 16.67% 15 1/4 25% 30 1/2 50% 40 2 /3 66.67% 45 3/4 75%
Hour(s) Parts of a Day Percent of a Day 1 1/24 4.17% 2 1/12 8.33% 6 1/4 25% 8 1/3 33.33% 12 1/2 50% 15 5/8 62.5% 18 3/4 75%
Month Parts of a Year Percent of a Year 1 1/12 8.33% 2 1/6 16.67% 3 1/4 25% 6 1/2 50%
360-day Year (30-day months)
Number of Day(s) Number of Month(s) Parts of a Year Percent of a Year 1 1/30 1/360 0.27% 10 1/3 1/36 2.78% 20 2 /3 1/18 5.56% 30 1 1/12 8.33% 60 2 1/6 16.67% 90 3 1/4 25% 120 4 1/3 33.33% 180 6 1/2 50%
MONETARY TABLES Business Math Handbook 13
Money Relationships
Unit Base Ratio Percent mil cent 1/10 10% mil. dollar 1/100 .1% cent nickel 1/5 20% cent dime 1/10 10% cent quarter 1/25 4% cent dollar 1/100 1% nickel dime 1/2 50% nickel quarter 1/5 20% nickel dollar 1/20 5% dime half dollar 1/5 20% dime dollar 1/10 10% quarter dollar 1/4 25%
International Monetary Units
COUNTRY BASIC UNIT COUNTRY BASIC UNIT Australia dollar India rupee Belgium franc Hungary forint Brazil cruzeiro Ireland pound Cambodia riel Israel pound Canada dollar Italy lira China yuan Japan yen Dominican Republic peso Korea won Egypt pound Kuwait dinar El Salvador colon Mexico peso France franc Philippines peso Germany deutsche mark Russia ruble Great Britain pound Saudi Arabia riyal Greece drachma South Africa rand United States dollar 14 Business Math Handbook
Compound Interest on $1.00 - 1/2%
Compound Present Present Value Amount of Period Interest Value of Annuity Annuity 1 1.0050 0.9950 0.9950 1.0000 2 1.0100 0.9901 1.9851 2.0050 3 1.0151 0.9851 2.9702 3.0150 4 1.0202 0.9802 3.9505 4.0301 5 1.0253 0.9754 4.9259 5.0503 6 1.0304 0.9705 5.8964 6.0755 7 1.0355 0.9657 6.8621 7.1059 8 1.0407 0.9609 7.8230 8.1414 9 1.0459 0.9561 8.7791 9.1821 10 1.0511 0.9513 9.7304 10.2280 11 1.0564 0.9466 10.6770 11.2792 12 1.0617 0.9419 11.6189 12.3356 13 1.0670 0.9372 12.5562 13.3973 14 1.0723 0.9326 13.4887 14.4643 15 1.0777 0.9279 14.4166 15.5365 16 1.0831 0.9233 15.3399 16.6142 17 1.0885 0.9187 16.2586 17.6973 18 1.0939 0.9141 17.1728 18.7858 19 1.0994 0.9096 18.0824 19.8797 20 1.1049 0.9051 18.9874 20.9791 21 1.1104 0.9006 19.8880 22.0840 22 1.1160 0.8961 20.7841 23.1945 23 1.1216 0.8916 21.6757 24.3104 24 1.1272 0.8872 22.5629 25.4320 25 1.1328 0.8828 23.4457 26.5591 26 1.1385 0.8784 24.3240 27.6919 27 1.1442 0.8740 25.1980 28.8304 28 1.1499 0.8697 26.0677 29.9746 29 1.1556 0.8653 26.9331 31.1245 30 1.1614 0.8610 27.7941 32.2801
Compound Interest on $1.00 - 1% Business Math Handbook 15
Compound Present Present Value Amount of Period Interest Value of Annuity Annuity 1 1.0100 0.9901 0.9901 1.0000 2 1.0201 0.9803 1.9704 2.0100 3 1.0303 0.9706 2.9410 3.0301 4 1.0406 0.9610 3.9020 4.0604 5 1.0510 0.9515 4.8534 5.1010 6 1.0615 0.9420 5.7955 6.1520 7 1.0721 0.9327 6.7282 7.2135 8 1.0829 0.9235 7.6517 8.2857 9 1.0937 0.9143 8.5660 9.3685 10 1.1046 0.9053 9.4713 10.4622 11 1.1157 0.8963 10.3676 11.5668 12 1.1268 0.8874 11.2551 12.6825 13 1.1381 0.8787 12.1337 13.8093 14 1.1495 0.8700 13.0037 14.9474 15 1.1610 0.8613 13.8650 16.0969 16 1.1726 0.8528 14.7179 17.2579 17 1.1843 0.8444 15.5622 18.4304 18 1.1961 0.8360 16.3983 19.6147 19 1.2081 0.8277 17.2260 20.8109 20 1.2202 0.8195 18.0455 22.0190 21 1.2324 0.8114 18.8570 23.2392 22 1.2447 0.8034 19.6604 24.4716 23 1.2572 0.7954 20.4558 25.7163 24 1.2697 0.7876 21.2434 26.9735 25 1.2824 0.7798 22.0231 28.2432 26 1.2953 0.7720 22.7952 29.5256 27 1.3082 0.7644 23.5596 30.8209 28 1.3213 0.7568 24.3164 32.1291 29 1.3345 0.7493 25.0658 33.4504 30 1.3478 0.7419 25.8077 34.7849
Compound Interest on $1.00 - 2% 16 Business Math Handbook
Compound Present Present Value Amount of Period Interest Value of Annuity Annuity 1 1.0200 0.9804 0.9804 1.0000 2 1.0404 0.9612 1.9416 2.0200 3 1.0612 0.9423 2.8839 3.0604 4 1.0824 0.9238 3.8077 4.1216 5 1.1041 0.9057 4.7134 5.2040 6 1.1262 0.8880 5.6014 6.3081 7 1.1487 0.8706 6.4720 7.4343 8 1.1717 0.8535 7.3255 8.5829 9 1.1951 0.8368 8.1622 9.7546 10 1.2190 0.8203 8.9826 10.9497 11 1.2434 0.8043 9.7868 12.1687 12 1.2682 0.7885 10.5753 13.4120 13 1.2936 0.7730 11.3483 14.6803 14 1.3195 0.7579 12.1062 15.9739 15 1.3459 0.7430 12.8492 17.2934 16 1.3728 0.7284 13.5777 18.6392 17 1.4002 0.7142 14.2918 20.0120 18 1.4282 0.7002 14.9920 21.4122 19 1.4568 0.6864 15.6784 22.8405 20 1.4859 0.6730 16.3514 24.2973 21 1.5157 0.6598 17.0112 25.7832 22 1.5460 0.6468 17.6580 27.2989 23 1.5769 0.6342 18.2922 28.8449 24 1.6084 0.6217 18.9139 30.4218 25 1.6406 0.6095 19.5234 32.0302 26 1.6734 0.5976 20.1210 33.6708 27 1.7069 0.5859 20.7069 35.3442 28 1.7410 0.5744 21.2812 37.0511 29 1.7758 0.5631 21.8443 38.7921 30 1.8114 0.5521 22.3964 40.5679
Compound Interest on $1.00 - 3%
Compound Present Present Value Amount of Business Math Handbook 17
Period Interest Value of Annuity Annuity 1 1.0300 0.9709 0.9709 1.0000 2 1.0609 0.9426 1.9135 2.0300 3 1.0927 0.9151 2.8286 3.0909 4 1.1255 0.8885 3.7171 4.1836 5 1.1593 0.8626 4.5797 5.3091 6 1.1941 0.8375 5.4172 6.4684 7 1.2299 0.8131 6.2303 7.6625 8 1.2668 0.7894 7.0197 8.8923 9 1.3048 0.7664 7.7861 10.1591 10 1.3439 0.7441 8.5302 11.4639 11 1.3842 0.7224 9.2526 12.8078 12 1.4258 0.7014 9.9540 14.1920 13 1.4685 0.6810 10.6350 15.6178 14 1.5126 0.6611 11.2961 17.0863 15 1.5580 0.6419 11.9379 18.5989 16 1.6047 0.6232 12.5611 20.1569 17 1.6528 0.6050 13.1661 21.7616 18 1.7024 0.5874 13.7535 23.4144 19 1.7535 0.5703 14.3238 25.1169 20 1.8061 0.5537 14.8775 26.8704 21 1.8603 0.5375 15.4150 28.6765 22 1.9161 0.5219 15.9369 30.5368 23 1.9736 0.5067 16.4436 32.4529 24 2.0328 0.4919 16.9355 34.4265 25 2.0938 0.4776 17.4131 36.4593 26 2.1566 0.4637 17.8768 38.5530 27 2.2213 0.4502 18.3270 40.7096 28 2.2879 0.4371 18.7641 42.9309 29 2.3566 0.4243 19.1885 45.2188 30 2.4273 0.4120 19.6004 47.5754
Compound Interest on $1.00 - 4%
Compound Present Present Value Amount of Period Interest Value of Annuity Annuity 18 Business Math Handbook
1 1.0400 0.9615 0.9615 1.0000 2 1.0816 0.9246 1.8861 2.0400 3 1.1249 0.8890 2.7751 3.1216 4 1.1699 0.8548 3.6299 4.2465 5 1.2167 0.8219 4.4518 5.4163 6 1.2653 0.7903 5.2421 6.6330 7 1.3159 0.7599 6.0021 7.8983 8 1.3686 0.7307 6.7327 9.2142 9 1.4233 0.7026 7.4353 10.5828 10 1.4802 0.6756 8.1109 12.0061 11 1.5395 0.6496 8.7605 13.4863 12 1.6010 0.6246 9.3851 15.0258 13 1.6651 0.6006 9.9856 16.6268 14 1.7317 0.5775 10.5631 18.2919 15 1.8009 0.5553 11.1184 20.0236 16 1.8730 0.5339 11.6523 21.8245 17 1.9479 0.5134 12.1657 23.6975 18 2.0258 0.4936 12.6593 25.6454 19 2.1068 0.4746 13.1339 27.6712 20 2.1911 0.4564 13.5903 29.7781 21 2.2788 0.4388 14.0292 31.9692 22 2.3699 0.4220 14.4511 34.2479 23 2.4647 0.4057 14.8568 36.6179 24 2.5633 0.3901 15.2470 39.0826 25 2.6658 0.3751 15.6221 41.6459 26 2.7725 0.3607 15.9828 44.3117 27 2.8834 0.3468 16.3296 47.0842 28 2.9987 0.3335 16.6631 49.9675 29 3.1187 0.3207 16.9837 52.9662 30 3.2434 0.3083 17.2920 56.0849
Compound Interest on $1.00 - 5%
Compound Present Present Value Amount of Period Interest Value of Annuity Annuity 1 1.0500 0.9524 0.9524 1.0000 Business Math Handbook 19
2 1.1025 0.9070 1.8594 2.0500 3 1.1576 0.8638 2.7232 3.1525 4 1.2155 0.8227 3.5459 4.3101 5 1.2763 0.7835 4.3295 5.5256 6 1.3401 0.7462 5.0757 6.8019 7 1.4071 0.7107 5.7864 8.1420 8 1.4775 0.6768 6.4632 9.5491 9 1.5513 0.6446 7.1078 11.0265 10 1.6289 0.6139 7.7217 12.5779 11 1.7103 0.5847 8.3064 14.2068 12 1.7959 0.5568 8.8632 15.9171 13 1.8856 0.5303 9.3936 17.7129 14 1.9799 0.5051 9.8986 19.5986 15 2.0789 0.4810 10.3796 21.5785 16 2.1829 0.4581 10.8378 23.6574 17 2.2920 0.4363 11.2741 25.8403 18 2.4066 0.4155 11.6896 28.1323 19 2.5270 0.3957 12.0853 30.5389 20 2.6533 0.3769 12.4622 33.0659 21 2.7860 0.3589 12.8211 35.7192 22 2.9253 0.3418 13.1630 38.5051 23 3.0715 0.3256 13.4886 41.4304 24 3.2251 0.3101 13.7986 44.5019 25 3.3864 0.2953 14.0939 47.7270 26 3.5557 0.2812 14.3752 51.1133 27 3.7335 0.2678 14.6430 54.6690 28 3.9201 0.2551 14.8981 58.4024 29 4.1161 0.2429 15.1411 62.3225 30 4.3219 0.2314 15.3724 66.4386
Compound Interest on $1.00 - 6%
Compound Present Present Value Amount of Period Interest Value of Annuity Annuity 20 Business Math Handbook
1 1.0600 0.9434 0.9434 1.0000 2 1.1236 0.8900 1.8334 2.0600 3 1.1910 0.8396 2.6730 3.1836 4 1.2625 0.7921 3.4651 4.3746 5 1.3382 0.7473 4.2124 5.6371 6 1.4185 0.7050 4.9173 6.9753 7 1.5036 0.6651 5.5824 8.3938 8 1.5938 0.6274 6.2098 9.8975 9 1.6895 0.5919 6.8017 11.4913 10 1.7908 0.5584 7.3601 13.1808 11 1.8983 0.5268 7.8869 14.9716 12 2.0122 0.4970 8.3838 16.8699 13 2.1329 0.4688 8.8527 18.8821 14 2.2609 0.4423 9.2950 21.0150 15 2.3966 0.4173 9.7122 23.2759 16 2.5404 0.3936 10.1059 25.6725 17 2.6928 0.3714 10.4773 28.2128 18 2.8543 0.3503 10.8276 30.9056 19 3.0256 0.3305 11.1581 33.7599 20 3.2071 0.3118 11.4699 36.7855 21 3.3996 0.2942 11.7641 39.9927 22 3.6035 0.2775 12.0416 43.3922 23 3.8197 0.2618 12.3034 46.9958 24 4.0489 0.2470 12.5504 50.8155 25 4.2919 0.2330 12.7834 54.8644 26 4.5494 0.2198 13.0032 59.1563 27 4.8223 0.2074 13.2105 63.7057 28 5.1117 0.1956 13.4062 68.5280 29 5.4184 0.1846 13.5907 73.6397 30 5.7435 0.1741 13.7648 79.0580 Business Math Handbook 21
Compound Interest on $1.00 - 7%
Compound Present Present Value Amount of Period Interest Value of Annuity Annuity 1 1.0700 0.9346 0.9346 1.0000 2 1.1449 0.8734 1.8080 2.0700 3 1.2250 0.8163 2.6243 3.2149 4 1.3108 0.7629 3.3872 4.4399 5 1.4026 0.7130 4.1002 5.7507 6 1.5007 0.6663 4.7665 7.1533 7 1.6058 0.6227 5.3893 8.6540 8 1.7182 0.5820 5.9713 10.2598 9 1.8385 0.5439 6.5152 11.9780 10 1.9672 0.5083 7.0236 13.8164 11 2.1049 0.4751 7.4987 15.7836 12 2.2522 0.4440 7.9427 17.8884 13 2.4098 0.4150 8.3576 20.1406 14 2.5785 0.3878 8.7455 22.5505 15 2.7590 0.3624 9.1079 25.1290 16 2.9522 0.3387 9.4466 27.8880 17 3.1588 0.3166 9.7632 30.8402 18 3.3799 0.2959 10.0591 33.9990 19 3.6165 0.2765 10.3356 37.3789 20 3.8697 0.2584 10.5940 40.9954 21 4.1406 0.2415 10.8355 44.8651 22 4.4304 0.2257 11.0612 49.0057 23 4.7405 0.2109 11.2722 53.4360 24 5.0724 0.1971 11.4693 58.1766 25 5.4274 0.1842 11.6536 63.2489 26 5.8074 0.1722 11.8258 68.6763 27 6.2139 0.1609 11.9867 74.4837 28 6.6488 0.1504 12.1371 80.6975 29 7.1143 0.1406 12.2777 87.3464 30 7.6123 0.1314 12.4090 94.4606 22 Business Math Handbook
Compound Interest on $1.00 - 8%
Compound Present Present Value Amount of Period Interest Value of Annuity Annuity 1 1.0800 0.9259 0.9259 1.0000 2 1.1664 0.8573 1.7833 2.0800 3 1.2597 0.7938 2.5771 3.2464 4 1.3605 0.7350 3.3121 4.5061 5 1.4693 0.6806 3.9927 5.8666 6 1.5869 0.6302 4.6229 7.3359 7 1.7138 0.5835 5.2064 8.9228 8 1.8509 0.5403 5.7466 10.6366 9 1.9990 0.5002 6.2469 12.4876 10 2.1589 0.4632 6.7101 14.4866 11 2.3316 0.4289 7.1390 16.6455 12 2.5182 0.3971 7.5361 18.9771 13 2.7196 0.3677 7.9038 21.4953 14 2.9372 0.3405 8.2442 24.2149 15 3.1722 0.3152 8.5595 27.1521 16 3.4259 0.2919 8.8514 30.3243 17 3.7000 0.2703 9.1216 33.7503 18 3.9960 0.2502 9.3719 37.4503 19 4.3157 0.2317 9.6036 41.4463 20 4.6610 0.2145 9.8181 45.7620 21 5.0338 0.1987 10.0168 50.4230 22 5.4365 0.1939 10.2007 55.4568 23 5.8715 0.1703 10.3711 60.8933 24 6.3412 0.1577 10.5288 66.7648 25 6.8485 0.1460 10.6748 73.1060 26 7.3964 0.1352 10.8100 79.9545 27 7.9881 0.1252 10.9352 87.3509 28 8.6271 0.1159 11.0511 95.3389 29 9.3173 0.1073 11.1584 103.9660 30 10.0627 0.0994 11.2578 113.2833 Business Math Handbook 23
Compound Interest on $1.00 - 9%
Compound Present Present Value Amount of Period Interest Value of Annuity Annuity 1 1.0900 0.9174 0.9174 1.0000 2 1.1881 0.8417 1.7591 2.0900 3 1.2950 0.7722 2.5313 3.2781 4 1.4116 0.7084 3.2397 4.5731 5 1.5386 0.6499 3.8897 5.9847 6 1.6771 0.5963 4.4859 7.5233 7 1.8280 0.5470 5.0330 9.2004 8 1.9926 0.5019 5.5348 11.0285 9 2.1719 0.4604 5.9952 13.0210 10 2.3674 0.4224 6.4177 15.1929 11 2.5804 0.3875 6.8052 17.5603 12 2.8127 0.3555 7.1607 20.1407 13 3.0658 0.3262 7.4869 22.9534 14 3.3417 0.2992 7.7862 26.0192 15 3.6425 0.2745 8.0607 29.3609 16 3.9703 0.2519 8.3126 33.0034 17 4.3276 0.2311 8.5436 36.9737 18 4.7171 0.2120 8.7556 41.3014 19 5.1417 0.1945 8.9501 46.0185 20 5.6044 0.1784 9.1285 51.1602 21 6.1088 0.1637 9.2922 56.7646 22 6.6586 0.1502 9.4424 62.8734 23 7.2579 0.1378 9.5802 69.5320 24 7.9111 0.1264 9.7066 76.7899 25 8.6231 0.1160 9.8226 84.7010 26 9.3992 0.1064 9.9290 93.3241 27 10.2451 0.0976 10.0266 102.7233 28 11.1672 0.0895 10.1161 112.9684 29 12.1722 0.0822 10.1983 124.1355 30 13.2677 0.0754 10.2737 136.3077 24 Business Math Handbook
Compound Interest on $1.00 - 10%
Compound Present Present Value Amount of Period Interest Value of Annuity Annuity 1 1.1000 0.9091 0.9091 1.0000 2 1.2100 0.8264 1.7355 2.1000 3 1.3310 0.7513 2.4869 3.3100 4 1.4641 0.6830 3.1699 4.6410 5 1.6105 0.6209 3.7908 6.1051 6 1.7716 0.5645 4.3553 7.7156 7 1.9487 0.5132 4.8684 9.4872 8 2.1436 0.4665 5.3349 11.4359 9 2.3579 0.4241 5.7590 13.5795 10 2.5937 0.3855 6.1446 15.9374 11 2.8531 0.3505 6.4951 18.5312 12 3.1384 0.3186 6.8137 21.3843 13 3.4523 0.2897 7.1034 24.5227 14 3.7975 0.2633 7.3667 27.9750 15 4.1772 0.2394 7.6061 31.7725 16 4.5950 0.2176 7.8237 35.9497 17 5.0545 0.1978 8.0216 40.5447 18 5.5599 0.1799 8.2014 45.5992 19 6.1159 0.1635 8.3649 51.1591 20 6.7275 0.1486 8.5136 57.2750 21 7.4002 0.1351 8.6487 64.0025 22 8.1403 0.1228 8.7715 71.4028 23 8.9543 0.1117 8.8832 79.5430 24 9.8497 0.1015 8.9847 88.4974 25 10.8347 0.0923 9.0770 98.3471 26 11.9182 0.0839 9.1609 109.1818 27 13.1100 0.0763 9.2372 121.1000 28 14.4210 0.0693 9.3066 134.2100 29 15.8631 0.0630 9.3696 148.6310 30 17.4494 0.0573 9.4269 164.4941 Business Math Handbook 25
Compound Interest on $1.00 - 11%
Compound Present Present Value Amount of Period Interest Value of Annuity Annuity 1 1.1100 0.9009 0.9009 1.0000 2 1.2321 0.8116 1.7125 2.1100 3 1.3676 0.7312 2.4437 3.3421 4 1.5181 0.6587 3.1024 4.7097 5 1.6851 0.5935 3.6959 6.2278 6 1.8704 0.5346 4.2305 7.9129 7 2.0762 0.4817 4.7122 9.7833 8 2.3045 0.4339 5.1461 11.8594 9 2.5580 0.3909 5.5370 14.1640 10 2.8394 0.3522 5.8892 16.7220 11 3.1518 0.3173 6.2065 19.5614 12 3.4985 0.2858 6.4924 22.7132 13 3.8833 0.2575 6.7499 26.2116 14 4.3104 0.2320 6.9819 30.0949 15 4.7846 0.2090 7.1909 34.4054 16 5.3109 0.1883 7.3792 39.1899 17 5.8951 0.1696 7.5488 44.5008 18 6.5436 0.1528 7.7016 50.3959 19 7.2633 0.1377 7.8393 56.9395 20 8.0623 0.1240 7.9633 64.2028 21 8.9492 0.1117 8.0751 72.2651 22 9.9336 0.1007 8.1757 81.2143 23 11.0263 0.0907 8.2664 91.1479 24 12.2392 0.0817 8.3481 102.1741 25 13.5855 0.0736 8.4217 114.4133 26 15.0799 0.0663 8.4881 127.9988 27 16.7386 0.0597 8.5478 143.0786 28 18.5799 0.0538 8.6016 159.8173 29 20.6237 0.0485 8.6501 178.3972 30 22.8923 0.0437 8.6938 199.0209 26 Business Math Handbook
Compound Interest on $1.00 - 12%
Compound Present Present Value Amount of Period Interest Value of Annuity Annuity 1 1.1200 0.8929 0.8929 1.0000 2 1.2544 0.7972 1.6901 2.1200 3 1.4049 0.7118 2.4018 3.3744 4 1.5735 0.6355 3.0373 4.7793 5 1.7623 0.5674 3.6048 6.3528 6 1.9738 0.5066 4.1114 8.1152 7 2.2107 0.4523 4.5638 10.0890 8 2.4760 0.4039 4.9676 12.2997 9 2.7731 0.3606 5.3282 14.7757 10 3.1058 9.3220 5.6502 17.5487 11 3.4785 0.2875 5.9377 20.6546 12 3.8960 0.2567 6.1944 24.1331 13 4.3635 0.2292 6.4235 28.0291 14 4.8871 0.2046 6.6282 32.3926 15 5.4736 0.1827 6.8109 37.2797 16 6.1304 0.1631 6.9740 42.7533 17 6.8660 0.1456 7.1196 48.8837 18 7.6900 0.1300 7.2497 55.7497 19 8.6128 0.1161 7.3658 63.4397 20 9.6463 0.1037 7.4694 72.0524 21 10.8038 0.0926 7.5620 81.6987 22 12.1003 0.0826 7.6446 92.5026 23 13.5523 0.0738 7.7184 104.6029 24 15.1786 0.0659 7.7843 118.1552 25 17.0001 0.0588 7.8431 133.3338 26 19.0401 0.0525 7.8957 150.3339 27 21.3249 0.0469 7.9426 169.3740 28 23.8839 0.0419 7.9844 190.6989 29 26.7499 0.0374 8.0218 214.5827 30 29.9599 0.0334 8.0552 241.3327 Business Math Handbook 27
Compound Interest on $1.00 - 13%
Compound Present Present Value Amount of Period Interest Value of Annuity Annuity 1 1.1300 0.8850 0.8850 1.0000 2 1.2769 0.7831 1.6681 2.1300 3 1.4429 0.6931 2.3612 3.4069 4 1.6305 0.6133 2.9745 4.8498 5 1.8424 0.5428 3.5172 6.4803 6 2.0820 0.4803 3.9975 8.3227 7 2.3526 0.4251 4.4226 10.4047 8 2.6584 0.3762 4.7988 12.7573 9 3.0040 0.3329 5.1317 15.4157 10 3.3946 0.2946 5.4262 18.4197 11 3.8359 0.2607 5.6869 21.8143 12 4.3345 0.2307 5.9176 25.6502 13 4.8980 0.2042 6.1218 29.9847 14 5.5348 0.1807 6.3025 34.8827 15 6.2543 0.1599 6.4624 40.4174 16 7.0673 0.1415 6.6039 46.6717 17 7.9861 0.1252 6.7291 53.7390 18 9.0243 0.1108 6.8399 61.7251 19 10.1974 0.0981 6.9380 70.7494 20 11.5231 0.0868 7.0248 80.9468 21 13.0211 0.0768 7.1015 92.4698 22 14.7138 0.0680 7.1695 105.4909 23 16.6266 0.0601 7.2297 120.2047 24 18.7881 0.0532 7.2829 136.8313 25 21.2305 0.0471 7.3300 155.6194 26 23.9905 0.0417 7.3717 176.8499 27 27.1093 0.0369 7.4086 200.8404 28 30.6335 0.0326 7.4412 227.9497 29 34.6158 0.0289 7.4701 258.5831 30 39.1159 0.0256 7.4957 293.1989 28 Business Math Handbook
Annual Percentage Rate Tables
Number of Payments 2.00% 2.25% 2.50% 2.75% 3.00% 3.25% 3.50% 3.75% 4.00% 4.25% 4.50% 4.75% 5.00% 5.25% 5.50% 5.75%
(FINANCE CHARGE PER $100 OF AMOUNT FINANCED)
1 0.17 0.19 0.21 0.23 0.25 0.27 0.29 0.31 0.33 0.35 0.37 0.40 0.42 0.44 0.46 0.48 2 0.25 0.28 0.31 0.34 0.38 0.41 0.44 0.47 0.50 0.53 0.56 0.59 0.63 0.66 0.69 0.72 3 0.33 0.38 0.42 0.46 0.50 0.54 0.58 0.63 0.67 0.71 0.75 0.79 0.83 0.88 0.92 0.96 4 0.42 0.47 0.52 0.57 0.63 0.68 0.73 0.78 0.83 0.89 0.94 0.99 1.04 1.10 1.15 1.20 5 0.50 0.56 0.63 0.69 0.75 0.81 0.88 0.94 1.00 1.07 1.13 1.19 1.25 1.32 1.38 1.44
6 0.58 0.66 0.73 0.80 0.88 0.95 1.02 1.10 1.17 1.24 1.32 1.39 1.46 1.54 1.61 1.68 7 0.67 0.75 0.84 0.92 1.00 1.09 1.17 1.25 1.34 1.42 1.51 1.59 1.67 1.76 1.84 1.93 8 0.75 0.85 0.94 1.03 1.13 1.22 1.32 1.41 1.51 1.60 1.69 1.79 1.88 1.98 2.07 2.17 9 0.84 0.94 1.04 1.15 1.25 1.36 1.46 1.57 1.67 1.78 1.88 1.99 2.09 2.20 2.31 2.41 10 0.92 1.03 1.15 1.26 1.38 1.50 1.61 1.73 1.84 1.96 2.07 2.19 2.31 2.42 2.54 2.65
11 1.00 1.13 1.25 1.38 1.51 1.63 1.76 1.88 2.01 2.14 2.26 2.39 2.52 2.64 2.77 2.90 12 1.09 1.22 1.36 1.50 1.63 1.77 1.91 2.04 2.18 2.32 2.45 2.59 2.73 2.87 3.00 3.14 13 1.17 1.32 1.46 1.61 1.76 1.91 2.05 2.20 2.35 2.50 2.64 2.79 2.94 3.09 3.24 3.39 14 1.25 1.41 1.57 1.73 1.89 2.04 2.20 2.36 2.52 2.68 2.84 2.99 3.15 3.31 3.47 3.63 15 1.34 1.51 1.67 1.84 2.01 2.18 2.35 2.52 2.69 2.86 3.03 3.20 3.37 3.54 3.71 3.88
16 1.42 1.60 1.78 1.96 2.14 2.32 2.50 2.68 2.86 3.04 3.22 3.40 3.58 3.76 3.94 4.12 17 1.51 1.70 1.89 2.08 2.26 2.46 2.65 2.84 3.03 3.22 3.41 3.60 3.79 3.98 4.18 4.37 18 1.59 1.79 1.99 2.19 2.39 2.59 2.79 2.99 3.20 3.40 3.60 3.80 4.00 4.21 4.41 4.61 19 1.67 1.89 2.10 2.31 2.52 2.73 2.94 3.15 3.37 3.58 3.79 4.01 4.22 4.43 4.65 4.86 20 1.76 1.98 2.20 2.42 2.65 2.87 3.09 3.31 3.54 3.76 3.98 4.21 4.43 4.66 4.88 5.11
21 1.84 2.08 2.31 2.54 2.77 3.01 3.24 3.47 3.71 3.94 4.18 4.41 4.65 4.88 5.12 5.35 22 1.93 2.17 2.41 2.66 2.90 3.14 3.39 3.63 3.88 4.12 4.37 4.62 4.86 5.11 5.36 5.60 23 2.01 2.27 2.52 2.77 3.03 3.28 3.54 3.79 4.05 4.31 4.56 4.82 5.08 5.33 5.59 5.85 24 2.10 2.36 2.62 2.89 3.15 3.42 3.69 3.95 4.22 4.49 4.75 5.02 5.29 5.56 5.83 6.10 25 2.18 2.46 2.73 3.01 3.28 3.56 3.84 4.11 4.39 4.67 4.95 5.23 5.51 5.79 6.07 6.35
26 2.27 2.55 2.84 3.12 3.41 3.70 3.99 4.27 4.56 4.85 5.14 5.43 5.72 6.01 6.31 6.60 27 2.35 2.65 2.94 3.24 3.54 3.84 4.13 4.43 4.73 5.03 5.34 5.64 5.94 6.24 6.54 6.85 28 2.43 2.74 3.05 3.36 3.67 3.97 4.28 4.59 4.91 5.22 5.53 5.84 6.15 6.47 6.78 7.10 29 2.52 2.84 3.16 3.47 3.79 4.11 4.43 4.76 5.08 5.40 5.72 6.05 6.37 6.70 7.02 7.35 30 2.60 2.93 3.26 3.59 3.92 4.25 4.58 4.92 5.25 5.58 5.92 6.25 6.59 6.92 7.26 7.60 Business Math Handbook 29
Annual Percentage Rate Tables
Number of Payments 6.00% 6.25% 6.50% 6.75% 7.00% 7.25% 7.50% 7.75% 8.00% 8.25% 8.50% 8.75% 9.00% 9.25% 9.50% 9.75%
(FINANCE CHARGE PER $100 OF AMOUNT FINANCED)
1 0.50 .052 0.54 0.56 0.58 0.60 0.62 0.65 0.67 0.69 0.71 0.73 0.75 0.77 0.79 0.81 2 0.75 0.78 0.81 0.84 0.88 0.91 0.94 0.97 1.00 1.03 1.06 1.10 1.13 1.16 1.19 1.22 3 1.00 1.04 1.09 1.13 1.17 1.21 1.25 1.29 1.34 1.38 1.42 1.46 1.50 1.55 1.59 1.63 4 1.25 1.31 1.36 1.41 1.46 1.51 1.57 1.62 1.67 1.72 1.78 1.83 1.88 1.93 1.99 2.04 5 1.50 1.57 1.63 1.69 1.76 1.82 1.88 1.95 2.01 2.07 2.13 2.20 2.26 2.32 2.39 2.45
6 1.76 1.83 1.90 1.98 2.05 2.13 2.20 2.27 2.35 2.42 2.49 2.57 2.64 2.72 2.79 2.86 7 2.01 2.09 2.18 2.26 2.35 2.42 2.52 2.60 2.68 2.77 2.85 2.94 3.02 3.11 3.19 3.28 8 2.26 2.36 2.45 2.55 2.64 2.74 2.83 2.93 3.02 3.12 3.21 3.31 3.40 3.50 3.60 3.69 9 2.52 2.62 2.73 2.83 2.94 3.05 3.15 3.26 3.36 3.47 3.57 3.68 3.79 3.89 4.00 4.11 10 2.77 2.89 3.00 3.12 3.24 3.35 3.47 3.59 3.70 3.82 3.94 4.05 4.17 4.29 4.41 4.42
11 3.02 3.15 3.28 3.41 3.53 3.66 3.79 3.92 4.04 4.17 4.30 4.43 4.56 4.68 4.81 4.94 12 3.28 3.42 3.56 3.69 3.83 3.97 4.11 4.25 4.39 4.52 4.66 4.80 4.94 5.08 5.22 5.36 13 3.53 3.68 3.83 3.98 4.13 4.28 4.43 4.58 4.73 4.88 5.03 5.18 5.33 5.48 5.63 5.78 14 3.79 3.95 4.11 4.27 4.43 4.59 4.75 4.91 5.07 5.23 5.39 5.55 5.72 5.88 6.04 6.20 15 4.05 4.22 4.39 4.56 4.73 4.90 5.07 5.24 5.42 5.59 5.76 5.93 6.10 6.28 6.45 6.62
16 4.30 4.48 4.67 4.85 5.03 5.21 5.40 5.58 5.76 5.94 6.13 6.31 6.49 6.68 6.86 7.05 17 4.56 4.75 4.95 5.14 5.33 5.52 5.72 5.91 6.11 6.30 6.49 6.69 6.88 7.08 7.27 7.47 18 4.82 5.02 5.22 5.43 5.63 5.84 6.04 6.25 6.45 6.66 6.86 7.07 7.28 7.48 7.69 7.90 19 5.07 5.29 5.50 5.72 5.94 6.15 6.37 6.58 6.80 7.02 7.23 7.45 7.67 7.89 8.10 8.32 20 5.33 5.56 5.78 6.01 6.24 6.46 6.69 6.92 7.15 7.38 7.60 7.83 8.06 8.29 8.52 8.75
21 5.59 5.83 6.07 6.30 6.54 6.78 7.02 7.26 7.50 7.74 7.97 8.21 8.46 8.70 8.94 9.18 22 5.85 6.10 6.35 6.60 6.84 7.09 7.34 7.59 7.84 8.10 8.35 8.60 8.85 9.10 9.36 9.61 23 6.11 6.37 6.63 6.89 7.15 7.41 7.67 7.93 8.19 8.46 8.72 8.98 9.25 9.51 9.77 10.04 24 6.37 6.64 6.91 7.18 7.45 7.73 8.00 8.27 8.55 8.82 9.09 9.37 9.64 9.92 10.19 10.47 25 6.63 6.91 7.19 7.48 7.76 8.04 8.33 8.61 8.90 9.18 9.47 9.75 10.04 10.33 10.62 10.90
26 6.89 7.18 7.48 7.77 8.07 8.36 8.66 8.95 9.25 9.55 9.84 10.14 10.44 10.74 11.04 11.34 27 7.15 7.46 7.76 8.07 8.37 8.68 8.99 9.29 9.60 9.91 10.22 10.53 10.84 11.15 11.46 11.77 28 7.41 7.73 8.05 8.36 8.68 9.00 9.32 9.64 9.96 10.28 10.60 10.92 11.24 11.56 11.89 12.21 29 7.67 8.00 8.33 8.66 8.99 9.32 9.65 9.98 10.31 10.64 10.97 11.31 11.64 11.98 12.31 12.65 30 7.94 8.28 8.61 8.96 9.30 9.64 9.98 10.32 10.66 11.01 11.35 11.70 12.04 12.39 12.74 13.09 30 Business Math Handbook
Annual Percentage Rate Tables
Number of Payments 10.00% 10.25% 10.50% 10.75% 11.00% 11.25% 11.50% 11.75% 12.00% 12.25% 12.50% 12.75% 13.00% 13.25% 13.50% 13.75%
(FINANCE CHARGE PER $100 OF AMOUNT FINANCED)
1 0.83 0.85 0.87 0.90 0.92 0.94 0.96 0.98 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.15 2 1.25 1.28 1.31 1.35 1.38 1.41 1.44 1.47 1.50 1.53 1.57 1.60 1.63 1.66 1.69 1.72 3 1.67 1.71 1.76 1.80 1.84 1.88 1.92 1.96 2.01 2.05 2.09 2.13 2.17 2.22 2.26 2.30 4 2.09 2.14 2.20 2.25 2.30 2.35 2.41 2.46 2.51 2.57 2.62 2.67 2.72 2.78 2.83 2.88 5 2.51 2.58 2.64 2.70 2.77 2.83 2.89 2.96 3.02 3.08 3.15 3.21 3.27 3.34 3.40 3.46
6 2.94 3.01 3.08 3.16 3.23 3.31 3.38 3.45 3.53 3.60 3.68 3.75 3.83 3.90 3.97 4.05 7 3.36 3.45 3.53 3.62 3.70 3.78 3.87 3.95 4.04 4.12 4.21 4.29 4.38 4.47 4.55 4.64 8 3.79 3.88 3.98 4.07 4.17 4.26 4.36 4.46 4.55 4.65 4.74 4.84 4.94 5.03 5.13 5.22 9 4.21 4.32 4.43 4.53 4.64 4.75 4.85 4.96 5.07 5.17 5.28 5.39 5.49 5.60 5.71 5.82 10 4.64 4.76 4.88 4.99 5.11 5.23 5.35 5.46 5.58 5.70 5.82 5.94 6.05 6.17 6.29 6.41
11 5.07 5.20 5.33 5.45 5.58 5.71 5.84 5.97 6.10 6.23 6.36 6.49 6.62 6.75 6.88 7.01 12 5.50 5.64 5.78 5.92 6.06 6.20 6.34 6.48 6.62 6.76 6.90 7.04 7.18 7.32 7.46 7.60 13 5.93 6.08 6.23 6.38 6.53 6.68 6.84 6.99 7.14 7.29 7.44 7.59 7.75 7.90 8.05 8.20 14 6.36 6.52 6.69 6.85 7.01 7.17 7.34 7.50 7.66 7.82 7.99 8.15 8.31 8.48 8.64 8.81 15 6.80 6.97 7.14 7.32 7.49 7.66 7.84 8.01 8.19 8.36 8.53 8.71 8.88 9.06 9.23 9.41
16 7.23 7.41 7.60 7.78 7.97 8.15 8.34 8.53 8.71 8.90 9.08 9.27 9.46 9.64 9.83 10.02 17 7.67 7.86 8.06 8.25 8.45 8.65 8.84 9.04 9.24 9.44 9.63 9.83 10.03 10.23 10.43 10.63 18 8.10 8.31 8.52 8.73 8.93 9.14 9.35 9.56 9.77 9.98 10.19 10.40 10.61 10.82 11.03 11.24 19 8.54 8.76 8.98 9.20 9.42 9.64 9.86 10.08 10.30 10.52 10.74 10.96 11.18 11.41 11.63 11.85 20 8.98 9.21 9.44 9.67 9.90 10.13 10.37 10.60 10.83 11.06 11.30 11.53 11.76 12.00 12.23 12.46
21 9.42 9.66 9.90 10.15 10.39 10.63 10.88 11.12 11.36 11.61 11.85 12.10 12.34 12.59 12.84 13.08 22 9.86 10.12 10.37 10.62 10.88 11.13 11.39 11.64 11.90 12.16 12.41 12.67 12.93 13.19 13.44 13.70 23 10.30 10.57 10.84 11.10 11.37 11.63 11.90 12.17 12.44 12.71 12.97 13.24 13.51 13.78 14.05 14.32 24 10.75 11.02 11.30 11.58 11.86 12.14 12.42 12.70 12.98 13.26 13.54 13.82 14.10 14.38 14.66 14.95 25 11.19 11.48 11.77 12.06 12.35 12.64 12.93 13.22 13.52 13.81 14.10 14.40 14.69 14.98 15.28 15.57
26 11.64 11.94 12.24 12.54 12.85 13.15 13.45 13.75 14.06 14.36 14.67 14.97 15.28 15.59 15.89 16.20 27 12.09 12.40 12.71 13.03 13.34 13.66 13.97 14.29 14.60 14.92 15.24 15.56 15.87 16.19 16.51 16.83 28 12.53 12.86 13.18 13.51 13.84 14.16 14.49 14.82 15.15 15.48 15.81 16.14 16.47 16.80 17.13 17.46 29 12.98 13.32 13.66 14.00 14.33 14.67 15.01 15.35 15.70 16.04 16.38 16.72 17.07 17.41 17.75 18.10 30 13.43 13.78 14.13 14.48 14.83 15.19 15.54 15.89 16.24 16.60 16.95 17.31 17.66 18.02 18.38 18.74 Business Math Handbook 31
Future Value of an Ordinary Annuity of $1.00
Period (n) 1.00% 1.25% 1.50% 2.00% 3.00% 4.00% 5.00% 6.00% 8.00% 9.00% 10.00% 12.00% 15.00% 18.00%
1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 2 2.01000 2.01250 2.01500 2.02000 2.03000 2.04000 2.05000 2.06000 2.08000 2.09000 2.10000 2.12000 2.15000 2.18000 3 3.03010 3.03766 3.04522 3.06040 3.09090 3.12160 3.15250 3.18360 3.24640 3.27810 3.31000 3.37440 3.47250 3.57240 4 4.06040 4.07563 4.09090 4.12161 4.18363 4.24646 4.31013 4.37462 4.50611 4.57313 4.64100 4.77933 4.99338 5.21543 5 5.10101 5.12657 5.15227 5.20404 5.30914 5.41632 5.52563 5.63709 5.86660 5.98471 6.10510 6.35285 6.74238 7.15421 6 6.15202 6.19065 6.22955 6.30812 6.46841 6.63298 6.80191 6.97532 7.33593 7.52333 7.71561 8.11519 8.75374 9.44197 7 7.21354 7.26804 7.32299 7.43428 7.66246 7.89829 8.14201 8.39384 8.92280 9.20043 9.48717 10.08901 11.06680 12.14152 8 8.28567 8.35889 8.43284 8.58297 8.89234 9.21423 9.54911 9.89747 10.63663 11.02847 11.43589 12.29969 13.72682 15.32700 9 9.36853 9.46337 9.55933 9.75463 10.15911 10.58280 11.02656 11.49132 12.48756 13.02104 13.57948 14.77566 16.78584 19.08585 10 10.46221 10.58167 10.70272 10.94972 11.46388 12.00611 12.57789 13.18079 14.48656 15.19293 15.93742 17.54874 20.30372 23.52131 11 11.56683 11.71394 11.86326 12.16872 12.80780 13.48635 14.20679 14.97164 16.64549 17.56029 18.53117 20.65458 24.34928 28.75514 12 12.68250 12.86036 13.04121 13.41209 14.19203 15.02581 15.91713 16.86994 18.97713 20.14072 21.38428 24.13313 29.00167 34.93107 13 13.80933 14.02112 14.23683 14.68033 15.61779 16.62684 17.71298 18.88214 21.49530 22.95338 24.52271 28.02911 34.35192 42.21866 14 14.94742 15.19638 15.45038 15.97394 17.08632 18.29191 19.59863 21.01507 24.21492 26.01919 27.97498 32.39260 40.50471 50.81802 15 16.09690 16.38633 16.68214 17.29342 18.59891 20.02359 21.57856 23.27597 27.15211 29.36092 31.77248 37.27971 47.58041 60.96527 16 17.25786 17.59116 17.93237 18.63929 20.15688 21.82453 23.65749 25.67253 30.32428 33.00340 35.94973 42.75328 55.71747 72.93901 17 18.43044 18.81105 19.20136 20.01207 21.76159 23.69751 25.84037 28.21288 33.75023 36.97370 40.54470 48.88367 65.07509 87.06804 18 19.61475 20.04619 20.48938 21.41231 23.41444 25.64541 28.13238 30.90565 37.45024 41.30134 45.59917 55.74971 75.83636 103.74028 19 20.81090 21.29677 21.79672 22.84056 25.11687 27.67123 30.53900 33.75999 41.44626 46.01846 51.15909 63.43968 88.21181 123.41353 20 22.01900 22.56298 23.12367 24.29737 26.87037 29.77808 33.06595 36.78559 45.76196 51.16012 57.27500 72.05244 102.44358 146.62797 21 23.23919 23.84502 24.47052 25.78332 28.67649 31.96920 35.71925 39.99273 50.42292 56.76453 64.00250 81.69874 118.81012 174.02100 22 24.47159 25.14308 25.83758 27.29898 30.53678 34.24797 38.50521 43.39229 55.45676 62.87334 71.40275 92.50258 137.63164 206.34479 23 25.71630 26.45737 27.22514 28.84496 32.45288 36.61789 41.43048 46.99583 60.89330 69.53194 79.54302 104.60289 159.27638 244.48685 24 26.97346 27.78808 28.63352 30.42186 34.42647 39.08260 44.50200 50.81558 66.76476 76.78981 88.49733 118.15524 184.16784 289.49448 25 28.24320 29.13544 30.06302 32.03030 36.45926 41.64591 47.72710 54.86451 73.10594 84.70090 98.34706 133.33387 212.79302 342.60349 26 29.52563 30.49963 31.51397 33.67091 38.55304 44.31174 51.11345 59.15638 79.95442 93.32398 109.18177 150.33393 245.71197 405.27211 27 30.82089 31.88087 32.98668 35.34432 40.70963 47.08421 54.69913 63.70577 87.35077 102.72313 121.09994 169.37401 283.56877 479.22109 28 32.12910 33.27938 34.48148 37.05121 42.93092 49.96758 58.40258 68.52811 95.33883 112.96822 134.20994 190.69889 327.10408 566.48089 29 33.45039 34.69538 35.99870 38.79223 45.21885 52.96629 62.32271 73.63980 103.96594 124.13536 148.63093 214.58275 377.16969 669.44745 30 34.78489 36.12907 37.53868 40.56808 47.57542 56.08494 66.43885 79.05819 113.28321 136.30754 164.49402 241.33268 434.74515 790.94799
32 Business Math Handbook
Present Value of an Ordinary Annuity of $1.00
Period (n) 1.00% 1.25% 1.50% 2.00% 3.00% 4.00% 5.00% 6.00% 8.00% 9.00% 10.00% 12.00% 15.00% 18.00%
1 0.99010 0.98765 0.98522 0.98039 0.97087 0.96154 0.95238 0.94340 0.92593 0.91743 0.90909 0.89286 0.86957 0.84746 2 1.97040 1.96312 1.95588 1.94156 1.91347 1.88609 1.85941 1.83339 1.78326 1.75911 1.73554 1.69005 1.62571 1.56564 3 2.94099 2.92653 2.91220 2.88388 2.82861 2.77509 2.72325 2.67301 2.57710 2.53129 2.48685 2.40183 2.28323 2.17427 4 3.90197 3.87806 3.85438 3.80773 3.71710 3.62990 3.54595 3.46511 3.31213 3.23972 3.16987 3.03735 2.85498 2.69006 5 4.85343 4.81784 4.78264 4.71346 4.57971 4.45182 4.32948 4.21236 3.99271 3.88965 3.79079 3.60478 3.35216 3.12717 6 5.79548 5.74601 5.69719 5.60143 5.41719 5.24214 5.07569 4.91732 4.62288 4.48592 4.35526 4.11141 3.78448 3.49760 7 6.72819 6.66273 6.59821 6.47199 6.23028 6.00205 5.78637 5.58238 5.20637 5.03295 4.86842 4.56376 4.16042 3.81153 8 7.65168 7.56812 7.48593 7.32548 7.01969 6.73274 6.46321 6.20979 5.74664 5.53482 5.33493 4.96764 4.48732 4.07757 9 8.56602 8.46234 8.36052 8.16224 7.78611 7.43533 7.10782 6.80169 6.24689 5.99525 5.75902 5.32825 4.77158 4.30302 10 9.47130 9.34553 9.22218 8.98259 8.53020 8.11090 7.72173 7.36009 6.71008 6.41766 6.14457 5.65022 5.01877 4.49409 11 10.36763 10.21780 10.07112 9.78685 9.25262 8.76048 8.30641 7.88687 7.13896 6.80519 6.49506 5.93770 5.23371 4.65601 12 11.25508 11.07931 10.90751 10.57534 9.95400 9.38507 8.86325 8.38384 7.53608 7.16073 6.81369 6.19437 5.42062 4.79322 13 12.13374 11.93018 11.73153 11.34837 10.63496 9.98565 9.39357 8.85268 7.90378 7.48690 7.10336 6.42355 5.58315 4.90951 14 13.00370 12.77055 12.54338 12.10625 11.29607 10.56312 9.89864 9.29498 8.24424 7.78615 7.36669 6.62817 5.72448 5.00806 15 13.86505 13.60055 13.34323 12.84926 11.93794 11.11839 10.37966 9.71225 8.55948 8.06069 7.60608 6.81086 5.84737 5.09158 16 14.71787 14.42029 14.13126 13.57771 12.56110 11.65230 10.83777 10.10590 8.85137 8.31256 7.82371 6.97399 5.95423 5.16235 17 15.56225 15.22992 14.90765 14.29187 13.16612 12.16567 11.27407 10.47726 9.12164 8.54363 8.02155 7.11963 6.04716 5.22233 18 16.39827 16.02955 15.67256 14.99203 13.75351 12.65930 11.68959 10.82760 9.37189 8.75563 8.20141 7.24967 6.12797 5.27316 19 17.22601 16.81931 16.42617 15.67846 14.32380 13.13394 12.08532 11.15812 9.60360 8.95011 8.36492 7.36578 6.19823 5.31624 20 18.04555 17.59932 17.16864 16.35143 14.87747 13.59033 12.46221 11.46992 9.81815 9.12855 8.51356 7.46944 6.25933 5.35275 21 18.85698 18.36969 17.90014 17.01121 15.41502 14.02916 12.82115 11.76408 10.01680 9.29224 8.64869 7.56200 6.31246 5.38368 22 19.66038 19.13056 18.62082 17.65805 15.93692 14.45112 13.16300 12.04158 10.20074 9.44243 8.77154 7.64465 6.35866 5.40990 23 20.45582 19.88204 19.33086 18.29220 16.44361 14.85684 13.48857 12.30338 10.37106 9.58021 8.88322 7.71843 6.39884 5.43212 24 21.24339 20.62423 20.03041 18.91393 16.93554 15.24696 13.79864 12.55036 10.52876 9.70661 8.98474 7.78432 6.43377 5.45095 25 22.02316 21.35727 20.71961 19.52346 17.41315 15.62208 14.09394 12.78336 10.67478 9.82258 9.07704 7.84314 6.46415 5.46691 26 22.79520 22.08125 21.39863 20.12104 17.87684 15.98277 14.37519 13.00317 10.80998 9.92897 9.16095 7.89566 6.49056 5.48043 27 23.55961 22.79630 22.06762 20.70690 18.32703 16.32959 14.64303 13.21053 10.93516 10.02658 9.23722 7.94255 6.51353 5.49189 28 24.31644 23.50252 22.72672 21.28127 18.76411 16.66306 14.89813 13.40616 11.05108 10.11613 9.30657 7.98442 6.53351 5.50160 29 25.06579 24.20002 23.37608 21.84438 19.18845 16.98371 15.14107 13.59072 11.15841 10.19828 9.36961 8.02181 6.55088 5.50983 30 25.80771 24.88891 24.01584 22.39646 19.60044 17.29203 15.37245 13.76483 11.25778 10.27365 9.42691 8.05518 6.56598 5.51681