Calculating the future value of your annuity
The future value of an annuity describes how much payments will be worth in the future, once they accumulate interest. This total is larger than the original principal invested.
Calculating an annuity’s future value will inform you of how much you would receive in the future at a given interest rate. It’s also used in lending to show the total cost of the loan, principal plus all interest paid.
One of the first things is to know the difference between an ordinary annuity and an annuity due. The difference is subtle. An ordinary annuity makes payments at the end of a payment period, while an annuity due requires payment at the beginning of a payment period. Why is this distinction important? If your payment comes on the last day of the month instead of the first day, you will receive your first payment a month sooner with an annuity due. On the other hand, interest accrues for an extra month with an ordinary annuity.
To calculate the future value of an ordinary annuity, you will need to know:
- The amount of each periodic payment (P)
- The number of periods over which payments will be made (N)
- An interest rate estimate or the actual annuity interest rate per period (R)
Then plug those numbers into the following formula:
Annuity Future Value = P x [((1+R)N – 1) / r]
Instead of doing the math yourself, there are calculators online you can use.
So let’s say you have an annuity that will pay you $1,000 a year for five years at an interest rate of 5 percent. Your annuity’s future value will be:
AFV = 1,000 x [((1 + .05)5 – 1) / .05]
A few things to note in case that looks confusing. First, percentages (such as interest rates) are expressed as decimals. So 5 percent becomes .05 (10 percent is .10; 100 percent is 1.00).
Second, algebraic equations dictate that totals inside parentheses are calculated together. So, the first step is to add 1 + .05, which equals 1.05.
AFV = 1,000 x [(1.05)5 – 1) / .05]
Next, the small 5 is an exponent, which means you multiply 1.05 by itself five times.
The final result is that the future value of this annuity is $5,525.
If you want to determine the future value of an annuity due, just take the future value of the ordinary annuity and add interest for one more payment period. Since the difference between the two is only one period of time, there won’t be much difference in the future values unless you’re using very large numbers. Therefore, unless you know for certain your payments will come at the beginning or end of the period, you can use either formula to obtain an accurate future annuity value.
To ensure accuracy, the formula’s variables should be consistent. That means if you’re using annual payment amounts, you should use annual interest rates. If you use monthly payment amounts and annual interest, you won’t obtain an accurate value. The easiest way to rectify a mismatch is to multiply your monthly payment by 12, your biennial payment by two or your quarterly payment by four, since most interest rates are expressed in annual terms. Otherwise, you can divide your annual rate by 12 to coincide with a monthly payment.