Here are some examples of the use of Time-Value-Of-Money calculations using the “FV of an annuity” function. This page relates to the discussion at Rates of Return. The inputs here refer to inputs into a financial calculator.
Problem #1: You have bought a life insurance contract with a policy value of $500,000. It requires you to pay $5,000 every year. In order to return an after-tax return on the ‘investment’ of 5%, by when must you be dead? | Inputs: FV = $500,000 Pmt = $5,000 i% = 5% |
CONCLUSION : You must die within 36.7 years. | Solve for: n = 36.7 |
Problem #2: You need $1 Million to retire (already adjusted for inflation) in 20 years. You can earn 8% after tax on your investments. How much must you save and add to the portfolio each year in order to accomplish that? | Inputs: FV = $1,000,000 n = 20 i% = 8% |
CONCLUSION : You must save $21,852 each years. | Solve for: Pmt = $21,852 |
Problem #3: You earn $40,000 in wages and save 12% earning 4%. Over a 10-year period, what rate of return must be earned, to end up in the same position, if you reduce your savings 2% to only 10% of wages. Start by finding the ending value when saving the 12%. | Inputs: n = 10 Pmt = $4,800 i% = 4% |
preliminary conclusion : You end up with $57,629 when you save at the higher rate. | Solve for: FV = $57,629 |
Now you know what the FV value is from one option, input that as a variable. Change the Pmts to reflect the lower 10% savings and solve for the interest rate. | Inputs: n = 10 Pmt = $4,000 FV = $57,629 |
CONCLUSION : The lower savings must be invested at 7.9%. | Solve for: i% = 7.9% |