An annuity is a stream of cash payments at regular intervals. For example, your car loan is an annuity you must pay over a certain period. You might someday have a retirement account that pays you a monthly annuity for the rest of your life. To find the value of an annuity, you can do calculations by hand or plug numbers into a spreadsheet or business calculator. A compound annuity table saves you some work when calculating an annuity’s value if you don't have access to a calculator or computer.
Compounding
Money earns interest over time. To compound interest is to add interest payments to the principal amount at regular intervals. For example, if you earn 6 percent annual interest on a savings account that compounds monthly, you multiply the current month-end balance by 6 percent divided by 12 months, or 0.5 percent. Add this interest to the balance, and repeat at the end of each month. In this way, you earn interest on your interest. You can also apply compounding to an annuity.
Compounded Annuity
A compounded annuity takes into account compound interest. You can use the interest rate per compounding period to figure the present value, future value and payment amounts of a compounded annuity. The mathematics for solving annuity problems is complex, but a compound annuity table lists several factors that help you solve these problems without a computer. The table is organized by the number of compounding periods and the compounding period’s interest rate. The table gives you present value and future value factors for an annuity of $1 per period at a given compounded interest rate.
Getting the Present Value
Suppose you’d like to know how much you’d have to sock away each month for 60 months to save up $7,000 -- the future value -- for a used car. You can earn 6 percent annual interest compounded monthly, which is 0.5 percent monthly. To figure the present value of a 60-period annuity, look up the single payment present value factor, also called a present worth factor, for 60 periods at 0.5 percent compounded interest per period. The result is 0.7414, which, when multiplied by $7,000, gives you a present value of $5,189.80. This is the lump sum you’d have to squirrel away today to equal $7,000 in 60 months.
Getting the Monthly Payments
To figure how much you must save each month, look up the present value factor for an annuity of 60 periods at 0.5 percent interest per period, which is 51.7256. When you divide this factor into the present value of $5,189.80, the result is a monthly payment of $100.33. Your total payments will equal 60 times $100.33, or $6,020. The remaining $980 of the $7,000 future value is compounded interest you earn on your annuity. Compound annuity tables, much like buggy whips and slide rules, have lost most of their relevance in the age of the Internet, where online calculators and spreadsheets are readily available to solve annuity problems quickly.
References
Resources
Writer Bio
Based in Greenville SC, Eric Bank has been writing business-related articles since 1985. He holds an M.B.A. from New York University and an M.S. in finance from DePaul University. You can see samples of his work at ericbank.com.