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.

Uniform annual series and present value

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 “P” be a single amount equivalent to the series, with “P” occurring one period before the first “A” payment. Note that although “P” is an abbreviation of “Present,” the single amount “P” may actually occur in the future as long as it occurs exactly one period before the first “A” payment.

The relationship between P and A is

P = A [ (1 + i) n – 1 ] / [ i (1 + i) n ]

Example: Suppose that a recent college graduate has $3,000 available as a down payment on a new car. The graduate can afford a uniform car loan payment of no more than $500 per month for 48 months, beginning 1 month from now. Interest is 6%, compounded monthly. What is the most that the graduate can spend today on a new car?