What is the formula for finding the future value of a growing annuity?


The future value of a growing annuity tells you just how much your money will grow after:

  • You have paid the regular contributions for the annuity
  • After the money has grown for several periods
  • After interest has been applied to the money on a compounded basis

In essence, what you will be doing is computing how much interest a certain payment will get after it has earned a specific interest rate compounded for a specific number of periods. Since most annuities involve numerous regular contributions made over time, what you are actually doing will be computing future value of each contribution, that is, the value of each contribution given the length of time it was paid and given the interest rate. Then, you will be adding all these future values to get the total value of an annuity at some point in time.

Whew! That was a mouthful!

To keep it simple, all you have to use to calculate the future value of an ordinary annuity is this formula:

Future Value = PMT [((1 + i)n - 1) / i]

Future Value = The Future Value of the Annuity
PMT = How much you'll be paying regularly in annuity contributions
i = interest rate applied for every period
n = the number of period covered

For instance, if you were contributing $10,000 yearly for an annuity that pays 6% compounded annually, what will its future value be in 5 years?

Using the formula, you have:

Future Value = 10,000 [((1+.06)5 - 1)/.06)
= 10,000 (5.637092)
= 56,370.92

The future value of your annual contributions of $10,000 applied with a compounded interest of 6% for 5 years is $56,370.92.

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