Q. Future Value of a Series of Equal Cash Flows?

Quite often a decision may result in the occurrence of cash flows of the same amount every year for a number of years consecutively, instead of a single cash flow. For example, a deposit of Rs. 1,000 each year is to be made at the end of each of the next 3 years from today. This may be referred to as an annuity of deposit of Rs. 1,000 for 3 years. An annuity is thus, a finite series of equal cash flows made at regular intervals. Calculation of the FV of an annuity can also be presented graphically as in figure below (rate of interest 10% compounded annually).

Calculation of Future Value ()f an Annuity of 3 Years (at r = 10-%)

In this case, each cash flow is to be compounded to find out its FV. The total of these FVs of all these cash flows will be the total FV of the annuity. The FV of an annuity also depends upon three variables, Le. the annual amount, the rate of interest and the time period. In order to find out the FV of an annuity, the pre-calculated mathematical table is available for various combinations of the rate of interest, r, and the time period, n.

In general terms, the future value of an annuity is given as:

FVA, A [(1+r) -1]

Where, F= Future value of an annuity which has duration of n years. Constant periodic flow. Interest rate per period. Duration of the annuity.
It is evident from the above that future value of an annuity depends upon three variables, A, rand n. The future value will vary if any of these three variables changes. For computation purposes, tables or calculators can be made use of.