A couple thinking about retirement decide to put aside $3,500 each year in a sav

Question

A couple thinking about retirement decide to put aside $3,500 each year in a savings plan that earns 9% interest. In 15 years they will receive a gift of $15,000 that also can be invested. a. How much money will they have accumulated 30 years from now? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Accumulated savings $ b. If their goal is to retire with $850,000 of savings, how much extra do they need to save every year? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Additional annual savings needed $

Explanation / Answer

a) FV of savings can be calculated using FV function

N = 30, PMT = 3,500, PV = 0, I/Y = 9% => Compute FV = $477,076.38

Similarly, the future value of gift

N = 15, PMT = 0, PV = 15,000, I/Y = 9% => Compute FV = $54,637.24

=> Accumulated savings = $531,713.62

b) Shortfall = 850,000 - 531,713.62 = 318,286.38

Additional savings can be calculated using PMT function

N = 30, I/Y = 9%, PV = 0, FV = 318,286.38

=> Compute PMT = $2,335.06 is the additional annual savings.

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