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.
The correct answer is: 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
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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