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 30th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw $130,000 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 7.5 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. a. If she starts making these deposits on her 31st 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

If she wants to be able to withdraw $130,000 from her savings account on each birthday for 20 years following her retirement.

The total amount that should be in her account at the end of 65 years = $ 130,000 X 20 years

The total amount that should be in her account at the end of 65 years = $ 2,600,000

Future value of the annuity = A [ ( 1+r)n -1 ] / r

$ 2,600,000 = A [ ( 1+0.075)35 -1 ] / 0.075

$ 195,000 = A [ ( 11.56 ) ]

A = $ 16,855.57 is to be deposited annually to be able to make the desired withdrawals at retirement

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