Annuity Formula

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Calculating an Annuity


Before we use the annuity formula, let's solve a short 3 year example the "long way". First we need the compound interest formula which is: Total = Principal × ( 1 + Rate )^years Now let's say the amount that we invest annually is $2,000 per year and the interest rate is 8%.

The $2,000 invested 3 years ago has become
$2,000 * (1.08)³ = $2,000 * 1.259712 = $2,519.424

The $2,000 invested 2 years ago has become
$2,000 * (1.08)² = $2,000 * 1.1664 = $2,332.80

The $2,000 invested 1 year ago becomes
$2,000 * (1.08)¹ = $2,000 * 1.08 = $2,160.00

Adding up all 3 yearly amounts, we obtain $7,012.22


As you can see, the mathematics of this can be a little cumbersome especially when the time involved gets larger. To make these calculations a little easier, there is a formula:

where the AMOUNT is the annual amount invested each year,
'n' is the number of years and
'r' is the annual rate of the investment.

So, we have:
$2,000 * { [(1 + .08)^{(3 + 1)} -1] ÷ .08 } — $2,000

$2,000 * { [1.36048896 -1] ÷ .08 } — $2,000

$2,000 * { .36048896 ÷ .08 } — $2,000

$2,000 * { 4.506112 } — $2,000

$9,012.224 -$2,000

$7,012.22

Which is the answer we obtained using the "long" method.

Luckily, you have a third and easier method - the annuity calculator !!!