How to Calculate the Future Value of an Annuity

By Mary Jane Sterling

In a finite math course, you will encounter a range of financial problems, such as how to calculate an annuity. An annuity consists of regular payments into an account that earns interest.

You can use a formula to figure out how much you need to contribute to it, for how long, and, most importantly, how much will be in your account when you want to start using the money.

You find the total amount accumulated in an annuity with

FNTMATH_1801

where P is the regular payment being made into the account, i is the interest rate per pay period (found with r/n), and m is the number of pay periods (found with nt). In this equation, r is the stated interest rate, n is the number of times each year that payments are made and interest is compounded, and t is the number of years.

You decide to participate in the annuity plan and commit to depositing $300 of your gross pay each month. The plan offers 7% interest on your investment. How much will you have in your account if you continue with this program for 30 years?

First, think about how much you’ll have contributed in 30 years. That’s $300 each month, 12 months each year, for 30 years, or

FNTMATH_1802

That’s a lot of money to contribute, but how far will $108,000 go toward expenses 30 years from now? Before deciding to contribute more, you find out what the interest on the investment will do. Using the formula,

FNTMATH_1803

you need to determine I by dividing 7% by 12. The value of i is about 0.00583333333. And the number of payments made or time periods is found by multiplying 12 times 30, which is 360. Substituting these values into the formula, you get

FNTMATH_1804

So, the interest takes your investment of $108,000 and more than triples it during the 30 years. But, again, you may think about increasing the amount contributed over the years of employment as you’re making more money.