  Retail Investor .org ### MATH EXAMPLES USING FV of an ANNUITY

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 = \$5,000i% = 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 = 20i% = 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 = \$4,800i% = 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 = \$4,000FV = \$57,629 CONCLUSION : The lower savings must be invested at 7.9%. Solve for:i% = 7.9% 