If we know the single amount (PV), the interest rate (i), and the number of periods of compounding (n), we can calculate the future value (FV) of the single amount. Calculations #1 through #5 illustrate how to determine the future value (FV) through the use of future value factors.
Calculation #1.
You make a single deposit of $100 today. It will remain invested for 4 years at 8% per year compounded annually. What will be the future value of your single deposit at the end of 4 years?
The following timeline plots the variables that are known and unknown:
Calculation using an FV factor:
At the end of 4 years, you will have $136 in your account.
Calculation #2.
Paul makes a single deposit today of $200. The deposit will be invested for 3 years at an interest rate of 10% per year compounded semiannually. What will be the future value of Paul’s account at the end of 3 years?
The following timeline plots the variables that are known and unknown:
Because the interest is compounded semiannually, we convert 3 years to 6 semiannual periods, and the annual interest rate of 10% to the semiannual rate of 5%.
Calculation using an FV factor:
At the end of 3 years, Paul will have $268 in his account.
Calculation #3.
Sheila invests a single amount of $300 today in an account that will pay her 8% per year compounded quarterly. Compute the future value of Sheila’s account at the end of 2 years.
The following timeline plots the variables that are known and unknown:
Because interest is compounded quarterly, we convert 2 years to 8 quarters, and the annual rate of 8% to thequarterly rate of 2%.
Calculation using an FV factor:
At the end of 2 years, Sheila will have $351.60 in her account.
Calculation #4.
You invest $400 today in an account that earns interest at a rate of 12% per year compounded monthly. What will be the future value at the end of 2 years?
The following timeline plots the variables that are known and unknown:
Because the interest is compounded monthly, we convert 2 years to 24 months, and the annual rate of 12% to the monthly rate of 1%.
Calculation using an FV factor:
At the end of 2 years, you will have $508 in your account.