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 40th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw $119,000 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, which offers 6.4 percent interest per year. She wants to make equal annual payments on each birthday into the account established at the credit union for her retirement fund.

If she starts making these deposits on her 41st 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?

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 40th birthday to cover her retirement needs. What amount does she have to deposit?

Suppose your friend

If she starts making these deposits on her 41st 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?

Explanation / Answer

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a. If she starts making these deposits on her 35th birthday and continues to make deposits until she is 65 (the last deposit will be on her 65th birthday), she must deposit $ annually to be able to make the desired withdrawals at retirement.

The present value of 15 $90,000 withdrawals discounted back 15 years at 9% is $612,977.80.
The thirty-one payments needed to reach this amount will be $2,017.38

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 34th birthday to cover her retirement needs. This deposit will have to be in the amount of $ .

The lump sum payment needed is the present value of $612,977.80 discounted back 32 years at 9%.
$16,310.53   

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