An annuity is a series of periodic payments. Examples of annuities include regular deposts to a savings account, montly car, mortgage, or insurance payments, and periodic payments to a person from a retirement fund. Although an annuity may vary in dollar amount, I will assume that an annuity involves a series of equal payments. Another assumption here is thata payments are all made at the end of a compounding period. The sum of an annuity or future value of an annuity can be found using the formula given below: we assume that the cash flow begins at the end of terms.

EXAMPLE 1

A person plans to deposit $10000 in a tax exempt savings plan at the end of this year and equal sum at the end of each following year. If interest is expected to be earned at the rate of 6% per year compounded annualy, to what sum will the investment grow at the time of fourth deposit?

SOLUTION

The present value of the series of annual payments can be found by using the formula mentioned above, where R=$10,000, i=0.06 and n=4

The answer is $43746.16

In cases where cash flows at the start of payment period, we call it annutiy due. The formula to compute the future value of annuity due where the cash flow begins at the beginning of terms is as follows.

If the deposits are made at the begining of the periods and interest is received immediately, we will have a sum of annuity different than the one we just computed. Lets see the results

The answer is $46370.93 which is higher than one we computed earlier.

Using MS Excel to compute Future Value of Annuities

Type   is the number 0 or 1 and indicates when payments are due. If type is omitted, it is assumed to be 0.