Future Value of Annuity

The future value of an annuity is the sum of the future values of all of the payments in the annuity. It is possible to take the FV of all cash flows and add them together, but this isn't really pragmatic if there are more than a couple of payments.

If you were to manually find the FV of all the payments, it would be important to be explicit about when the inception and termination of the annuity is. For an annuity-due, the payments occur at the beginning of each period, so the first payment is at the inception of the annuity, and the last one occurs one period before the termination.

For an ordinary annuity, however, the payments occur at the end of the period. This means the first payment is one period after the start of the annuity, and the last one occurs right at the end. There are different FV calculations for annuities due and ordinary annuities because of when the first and last payments occur.

There are some formulas to make calculating the FV of an annuity easier. For both of the formulas we will discuss, you need to know the payment amount (m, though often written as pmt or p), the interest rate of the account the payments are deposited in (r, though sometimes i), the number of periods per year (n), and the time frame in years (t).

The formula for an ordinary annuity is as follows:

$\displaystyle{A=\frac{m[(1+r/n)^{nt}-1]}{r/n}}$

where m is the payment amount, r is the interest rate, n is the number of periods per year, and t is the length of time in years.

In contrast, the formula for an annuity-due is as follows:

$\displaystyle{A=\frac{m[(1+r/n)^{nt+1}-1]}{r/n}-m}$

Provided you know m, r, n, and t, therefore, you can find the future value (FV) of an annuity.