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Calculating Annuity Payments 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 $15,000 from her savings account on each
birthday for 12 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 9 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), what amount must she 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 36th birthday to cover her
retirement needs. What amount would she have to deposit?
c. Suppose your friend’s employer will contribute $250 into the
account every year as part of the company’s profit-sharing plan. In
addition, your friend expects a $10,000 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?
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