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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 = $5,000
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%