What is the future value of an annuity
The future value of an annuity is the value of a group of recurring payments on a specified date in the future. These recurring payments are known as annuities and are calculated using a specific formula.
The future value of an annuity measures how much you would have in the future at a specified rate of return or discount rate. Future cash flows from the annuity increase at the indicated discount rate, so a higher discount rate translates into a higher future value for the annuity.
Key points to remember
- The future value of an annuity is a way to calculate how much money an annuity, which will pay in the future, is worth today.
- The formula for calculating the future value of an annuity must take into account the fact that the money received today has more value than money in the future.
- In an ordinary annuity, payments are made at the end of each agreed period. In a due annuity, payments are made at the start of each period.
Formula and calculation of the future value of an annuity
Because of the time value of money, the cash flows received today are worth more than the same cash flows in the future. The money received today can be invested now and grow over time. In the same logic, receiving $ 5,000 today is worth more than receiving $ 1,000 a year for five years. The lump sum invested today is worth more at the end of the five years than the additional investments of $ 1,000 each year, even if they are invested at the same interest rate.
Annuities are often purchased by retirees to supplement social security and other forms of retirement income.
Example of calculating the current value of an ordinary annuity
The formula for the future value of an ordinary annuity is as follows:
P = PMT x (((1 + r) ^ n – 1) / r)
P = the future value of a stream of annuities
PMT = dollar amount of each annuity payment
r = the interest rate (also called the discount rate)
n = the number of periods during which payments will be made
Suppose a portfolio manager decides to invest $ 125,000 per year over the next five years in an investment he plans to make up to 8% per year. The expected future value of this payment stream using the above formula is:
Future value of the annuity = $ 125,000 x (((1 + 0.08) ^ 5-1) / 0.08) = $ 733,325
This formula is for the future value of an ordinary annuity, that is, when payments are made at the end of the period in question. With an annuity due, payments are made at the start of the period in question. To find the future value of an annuity due, simply multiply the above formula by a factor (1 + r):
P = PMT x (((1 + r) ^ n – 1) / r) x (1 + r)
If the above example was an annuity due, its future value would be calculated as follows:
Future value of the annuity due = $ 125,000 x (((1 + 0.08) ^ 5-1) / 0.08) x (1 + 0.08) = $ 791,991.