Q:

Janet Spears is planning to retire in 7 years and plans to start saving \$15,000 a year beginning at the end of this year until the date she retires. She currently has \$280,000 at the bank. Once she retires, she plans to start redeeming \$21,000 each year for 26 years. If she can expect to earn 9% before her retirement and 7.5% after her retirement, which of the following answers would best describe her situation?
a) On her retirement date, she'll have a surplus of \$412,568.
b) On her retirement date, she'll have a surplus of \$35,245.
c) On her retirement date, she'll have a surplus of \$142,895.
d) On her retirement date, she'll have a deficit of \$35,245.

A:

Step 1: How much will she have accumulated her wealth by the time she retires?

PV = 280,000; PMT = 15,000; N = 7; I = 9%

Therefore, FV = 649.875

Step 2: How much will she need by her retirement date in order to finance her retirement
income?

PMT = 21,000; N = 26; I = 7.5%

Therefore, PV = 237,289

Step 3: Surplus/Shortfall at retirement

= (what she'll have) - (what she'll need)

= 649,857 - 237,289

Surplus = 412,568

2005 CFA Level 1 LOS: 2.1.A.a-2.1.A.c

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