How to Calculate the Starting Value of an Annuity

By Mary Jane Sterling

In a finite math course, you’ll often be asked to use mathematical formulas to solve real-world problems. A good example of this is calculating the starting value of an annuity.

Say that you’re planning an around-the-world-trip, and your big concern is how to fund this adventure. One way is to have a fund from which you can withdraw a certain amount of money at regular intervals and have just enough money when you’re finished, where the fund goes down to zero.

You’re going to sail around the world on your 40-foot sloop. You’re estimating it will take seven years, with all the visiting, sightseeing, and other activities. You need to set up an annuity from which you can withdraw monthly amounts to help with the expenses. You want to have $2,000 available each month and have the balance be zero at the end of the seven years. How much should you put in your annuity account?

The present value of an annuity is determined with

FNTMATH_1901

where V is the value or amount needed to be deposited into the account, P is the payment or amount withdrawn periodically, i is the interest each time period, and m is the number of time periods.

You find a broker who can get you 9% interest on your deposit. You want to withdraw monthly, so that will be 7 times 12, or 84 payments or time periods. The interest rate each time period is found with r/n, which is 9% divided by 12, or 0.0075%. Using the formula for the present value, that comes to

FNTMATH_1902

You need to deposit more than $124,000 to be able to make your regular withdrawals and have a balance of zero at the end of seven years. What is $2,000 per month for seven years, if you aren’t withdrawing from an annuity? Multiply

FNTMATH_1903

Sounds like a good deal—if you can come up with that initial deposit.