This is a classic retirement problem. A time line will help in solving it. Your

Question

This is a classic retirement problem. A time line will help in solving it. Your friend is celebrating her 35th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw $128,000 from her savings account on each birthday for 20 years following her retirement, the first withdrawal will be on her 66th birthday. Your friend intends to invest her money in the local credit union, She wants to make equal annual payments on each birthday into which offers 7.3 percent interest per year the account established at the credit union for her retirement fund a. If she starts making these deposits on her 36th birthday and continues to make deposits until she is 65 (the last deposit will be on her 65th birthday), what amount must she deposit annually to be able to make the desired withdrawals at retirement? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Annual deposit amount b. Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump sum payment on her 35th birthday to cover her retirement needs. What amount does she have to deposit? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Amount deposit c. Suppose your friend's employer will contribute $3,800 to the account every year as part of the company's profit-sharing plan. In addition, your friend expects a $178,000 distribution from a family trust fund on her 55th birthday, which she will also put into the retirement account. What amount must she deposit annually now to be able to make the desired withdrawals at retirement? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Annual deposit amount

Explanation / Answer

Soln : a) Let x be the amount she start saving from her 36th birthday, to get the amount $128000 on each birthday after 65th birthday.

We can calculate it by taking PV of all withdrwal at t = 65, and FW of all amount x in 30 years equal to that value.

Considering the interest rate all years as 7.3%

Value of withdrawls at 65 years of age = 128000 *(P/A,7.3%,20) = 128000*((1.073)20 -1)/0.073*(1.073)20 = 128000*10.35 = $1324982

Now, the value x in each year should be equal to this value, i.e.:

x*(F/A, 7.3%,30) = 1324982

x*((1.073)30 -1)/0.073 = 1324982

x = 1324982/99.72 = 13288 (approx.)

Amount to be saved by her from 36th birthday = $13288

b) As we have calculated above the amount of money at 65th birthday from all the withdrawals = $1324982 = lumpsum money required to deposit.

c) Now, $3800 being deposited by the company, Let X be the amount she needs to save.

Again we will equalise the cash flows :

(X+3800)*(F/A, 7.3%,30) + 178000 *1.07310 = 1324982

(X+3800)*99.72 = 964886.89

On solving we, get X = 5876.35

Amount to be deposited in savings = $5876.35

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