Question

Chris Jones wishes to have $400,000 in a retirement fund 25 years from now. He can create the retirement fund by making a single lump-sum deposit today. Use next table to solve the following problems.

A. If he can earn 7 percent on his investments, how much must Chris deposit today to create the retirement fund? Round PV-factor to three decimal places. Round your answer to the nearest cent.

Calculate your answer based on the PV-factor.

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Calculate your answer based on the financial calculator.

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If he can earn only 5 percent on his investments? Round PV-factor to three decimal places. Round your answer to the nearest cent.
Calculate your answer based on the PV-factor.

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Calculate your answer based on the financial calculator.

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B. If, upon retirement in 25 years, Chris plans to invest the $400,000 in a fund that earns 5 percent, what is the maximum annual withdrawal he can make over the following 20 years? Round the answer to the nearest cent. Round PVA-factor to three decimal places.
Calculate your answer based on the PVA-factor.

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Calculate your answer based on the financial calculator.

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C. How much would Chris need to have on deposit at retirement to annually withdraw $55,000 over the 20 years if the retirement fund earns 5 percent? Round the answer to the nearest cent. Round PVA-factor to three decimal places.
Calculate your answer based on the PVA-factor.

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Calculate your answer based on the financial calculator.

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D. To achieve his annual withdrawal goal of $55,000 calculated in part c, how much more than the amount calculated in part a must Chris deposit today in an investment earning 5 percent annual interest? Round PVA-factor to three decimal places. Round your answer to the nearest cent. If an amount is zero, enter "0".

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Answer 1

A. $ 73,600 if he can earn 7 % on his investments.

$ 118,000 if he can earn only 5 % on his investments.

PV _{7%, n = 25} = ( 1 / 1.07 ) ²⁵ = 0.184

Present value of $ 400,000 = $ 400,000 x 0.184 = $ 73,600

PV _{5 %},_n=25 = ( 1 / 1.05 ) ²⁵ = 0.295

Present value of $ 400,000 = $ 400,000 x 0.295 = $ 118,000

B. Maximum annual withdrawal Chris can make over the following 20 years : $ 32,097.58

PVA _{5%, n=20} = [ { 1 - ( 1 / 1.05 ) ²⁰ } / 0.05 ] = 12.462

Present Value of an Annuity = Annuity x PVA

Annuity = $ 400,000 / 12.462 = $ 32,097.58

C. Chris would need to have $ 685,410 at retirement to annually withdraw $ 55,000.

D. $ 84,195.95 more needs to be deposited today.