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.