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 $125,000 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 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 36th 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.
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. This deposit will have to be in the amount of $_____ .
c. Suppose your friend's employer will contribute $3500 to the account every year as part of the company's profit-sharing plan. In addition, your friend expects a $175,000 distribution from a family trust fund on her 55th birthday, which she will also put into the retirement account. She must deposit $_________ annually now to be able to make the desired withdrawals at retirement.

Answer 1

Answer:

a. $21,725.65

b. $19,385

c. 27,421.32

Explanation:

Savings = 125,000

Annuity Formula :

$(\frac{1}{1.07})^{30}$ [  $\frac{125,000}{0.07}$ ( $1 - \frac{1}{1.07 ^}^{20}$ ) ] = $\frac{A}{0.07}$ ( $1 - \frac{1}{0.07 ^ } ^{30}$ )

Solving the equation we get,

A  = $21,725.65