Problem III (20 Points) Part (a) Bill Smith is 30 years old and decides to start

Question

Problem III (20 Points) Part (a) Bill Smith is 30 years old and decides to start saving for his retirement. Bill plans to put $15,000 into an investment account at the end of every year for the next 35 years. If the investment account earns 8% annually: how much money will Bill have in his account at the end of 35 years? Part (b) Assume Bill accumulated $2,200,000 at the age of 65. How much could Bill withdraw from the investment on the first day of each year for the next 25 years? Assume the investment account earned 9% annually Part (c) Assume Bill accumulated $2,500,000 at the age of 65. He has decided not to withdraw or deposit any funds into his investment account and plans to leave the money to his children in 20 years. How much money will Bill's children receive assuming the investment account earned 6% annually for the 20 year period? Show all work. If you use a table: state the table used, # of periods & interest rate. If you use a calculator show key strokes; i.e. 8-N, 4-1, 20-PMT, So-PV etc. ANSWER IN THE SPACE PROVIDED ON THE NEXT PAGE

Explanation / Answer

Part a.

Future Value of annuity for next 35 years @ 8%.

Interest rate = 8%, number of period = 35 years

FVIF = P [(1+r)^n -1)/r]

= 15000 [(1+0.08)^35 - 1)/0.08]

= 15000 (172.3168)

= $2,584,752 approx.

Part b.

Bill can reduce the following each year for next 25 years

Interest = 9% Number of years = 25 years

Present value of annuity due = PV [r/1 - (1+r)^-n] * 1/(1+r)]

= 2200000 [(0.09/1 - (1+0.09)^-25] * [1/(1+0.09)]

= $205,480.51

So, he can withdraw $205,480.51 on the first day of each year for next 25 years.

Part c.

Future Value for next 20 years @ 6%.

Interest rate = 6%, number of period = 20 years

Future value of single payment = P (1+r)^n

= 2500000 (1+0.06)^20

= 2500000 (3.2071)

= $8,017,838.68

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