Harry plans to start saving to provide for his retirement. Beginning one month f

Question

Harry plans to start saving to provide for his retirement. Beginning one month from now, he will begin depositing a fixed amount each month into a retirement savings account that will earn 8.4% APR, compounded monthly. He will make these deposits for 35 years. Then, one month after making his final deposit, he will begin withdrawing $5,000 each month, and continue doing so for 20 years. The fund will continue to earn 8.4% APR compounded monthly.

Use this information to answer sections (a) and (b) below. PLEASE SHOW ALL WORK.

a. How much does Harry need to have saved 30-days prior to his first withdrawal in order to meet his retirement goal?

b. How much must Harry deposit into his account each month in order to achieve his retirement goal?

Explanation / Answer

Answer:

a)Present value of an anuuity = Annuity* {(1+interest rate)no of periods-1}/Interest rate*(1+interest rate)no of periods

                                         = $5,000*{(1+0.084/12)20*12-1}/(0.084/12)*{(1+0.084/12)20*12

                                         = $5,000*(4.334/0.0373)= $580,347.26 (ans)

b) Future value of an Annuity = Annuity* {(1+interest rate)no of periods-1}/Interest rate

            => $580,347.26 = Annuity {(1+0.084/12)35*12-1}/(0.084/12)

            => $580,347.26 = Annuity {(1.007)420-1}/0.007

             => $580,347.26 = Annuity *2531.87

           => Annuity = $580,347.26/2,531.87 = $229.22 (ans)

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