f/a annual

Suppose that there is a series of "n" uniform payments, uniform in amount and uniformly spaced, such as a payment every year.

Let "A" be the amount of each uniform payment.

Let "F" be a future, single amount equivalent to the series, with "F" occurring at the same time as the last "A" payment. Then the relationship between F and A is:

F = A [ (1 + i) ⁿ - 1 ] / i

Example: If $100 is invested at the end of each year for the next 10 years in a savings account that pays 5% interest, how much will be in the account immediately after the tenth payment?

F is the unknown.

A = $100 per year

i = 5%, understood to be 5% per year, compounded annually.

n = 10 years

F = A [ (1 + 0.05) ¹⁰ - 1 ] / 0.05

= $100 [ (1.05) ¹⁰ - 1 ] / 0.05

= $100 (0.6289 / 0.05) = $1,258.

Or, using the 5% interest table, which is quicker:

F = A (F/A,5%,10) = $100 ( 12.578 ) = $1,258.