What Is the Future Value of an Annuity
The future value of an annuity is the value of a group of recurring payments at a specified date in the future. These regularly recurring payments are known as an annuity 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. The annuity's future cash flows grow at the stated discount rate, so a higher discount rate results in a higher future value for the annuity.
- The future value of an annuity is a way of calculating how much money an annuity, which pays in the future, is worth today.
- The formula for calculating the future value of an annuity must take into account the fact that cash received today is more valuable than cash in the future.
- In an ordinary annuity, payments are made at the end of each agreed-upon period. In an annuity due, payments are made at the beginning of each period.
Formula and Calculation of Future Value of an Annuity
Because of the time value of money, 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. By the same logic, receiving $5,000 today is worth more than getting $1,000 per year for five years. The lump-sum invested today is worth more at the end of the five years than the incremental investments of $1,000 each year, even if they are invested at the exact same interest rate.
Ordinary Annuity Present Value Example Calculation
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 an annuity stream
PMT = the dollar amount of each annuity payment
r = the interest rate (also known as the discount rate)
n = the number of periods in which payments will be made
Assume a portfolio manager decides to invest $125,000 per year for the next five years into an investment that he or she expects to compound at 8% per year. The expected future value of this payment stream using the above formula is:
Future value of annuity = $125,000 x (((1 + 0.08) ^ 5 - 1) / 0.08) = $733,325
This formula is for the future value of an ordinary annuity, which is when payments are made at the end of the period in question. With an annuity due, the payments are made at the beginning of the period in question. To find the future value of an annuity due, simply multiply the above formula by a factor of (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:
Future value of annuity due = $125,000 x (((1 + 0.08) ^ 5 - 1) / 0.08) x (1 + 0.08) = $791,991.