Future Value of an Annuity
The present value of an annuity is based on the concept of the time value of money. The time value of money means that money is worth more the sooner you have it. Payments that are scheduled to be received in the future are worth less today because of the uncertainty of future economic conditions. Current payments have more value because they can be invested in the meantime.
The future value of an annuity is the total value that annuity payments will be worth at a specific point in the future. It is the value of a group of recurring payments at a specific date in the future, given a particular rate of return. The higher the rate of return is, the greater the annuity’s future value will be.
The future value of an annuity differs from the present value of an annuity, as the present value gives you the current value of future annuity payments.
Knowing the future value of your annuity is useful for annuitants who want to plan for retirement. By knowing how much annuity payments will be worth, annuitants can accurately plan how to allocate other sources of income and how to handle other investments.
How to Calculate the Future Value of an Annuity
Since the future value of an annuity is a way of calculating how much money a series of payments will be worth in the future, there is a formula that can be used to determine future value. The formula can be used as long as the periodic payment amount, interest rate and total number of payments are known information.
Ordinary annuities are annuities where the payments are made at the end of each pay period. The following is the formula for an ordinary annuity:
P = PMT x ((1+r)^n —1) / r
P= future value of an annuity stream
PMT= the periodic payment
r= the interest rate per period
n= the total number of periods
For instance, assume someone decides to invest $100,000 per year for the next five years in an annuity they expect to compound at 7% per year. The expected future value of this payment stream using the above formula is as follows:
P = 50,000 x ((1 + .07)^5 –1) / .07
Future value = $287,536.95
The opposite of an ordinary annuity is an annuity due, which is an annuity that makes payments at the beginning of each pay period. The formula is slightly different to calculate the future value for an annuity due. To find the future value of an annuity due, simply multiply the formula above by a factor of (1 + r):
P = PMT x (((1+r)^n —1) / r) x (1 + r)
If the same example as above were an annuity due, its future value would be calculated as follows:
P = 100,000 x )((1 + .07)^5 –1) / .07) x (1 + .07)
Future value = $307,664.54
If all other factors are held equal, the future value of an annuity due will be greater than the future value of an ordinary annuity. This is because annuity dues have an extra period of time to accrue interest since the payments are not made until the end of the pay period. This is demonstrated through the examples above, as the future value of the annuity due was $307,664.54, and the future value of an ordinary annuity was only $287,536.95 given the same numbers.
Special thanks in preparing this summary of “What is The Future Value of an Annuity?” goes to Bob Carlson, leader of the Retirement Watch advisory service and chairman of the Board of Trustees of Virginia’s Fairfax County Employees’ Retirement System with more than $4 billion in assets.