MATH EXAMPLES USING FV of an ANNUITY
Here are some examples of the use of TimeValueOfMoney 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 aftertax 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 10year 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% 

