A 40-year-old individual establishes a retirement account that is expected to ea
ID: 2639232 • Letter: A
Question
A 40-year-old individual establishes a retirement account that is expected to earn 7 percent annually. Contributions will be $2,000 annually at the beginning of each year. Initially, the saver expects to start drawing on the account at age 60.a) How much will be in the account when the saver is age 60?
b) If this investor found a riskier investment that offered 10 percent, how much in ad-
ditional funds would be earned?
c) The investor selects the 10 percent investment and retires at the age of 60. How
much can be drawn from the account at the beginning of each year if life expec-
tancy is 85 and the funds continue to earn 10 percent? A 40-year-old individual establishes a retirement account that is expected to earn 7 percent annually. Contributions will be $2,000 annually at the beginning of each year. Initially, the saver expects to start drawing on the account at age 60.
a) How much will be in the account when the saver is age 60?
b) If this investor found a riskier investment that offered 10 percent, how much in ad-
ditional funds would be earned?
c) The investor selects the 10 percent investment and retires at the age of 60. How
much can be drawn from the account at the beginning of each year if life expec-
tancy is 85 and the funds continue to earn 10 percent?
Explanation / Answer
a) How much will be in the account when the saver is age 60:
Future Value = annual payment*((1+rate)^(no. of years)-1)/rate
=2000*((1+7%)^(20)-1)/7%
=$81990.98
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b) If this investor found a riskier investment that offered 10 percent, how much in ad-ditional funds would be earned:
Future value when rate is 10% = 2000*((1+10%)^(20)-1)/10%
=$114550
Addition amount earned = $(114550-81990.98)
=$32559.02
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c) How much can be drawn from the account at the beginning of each year :
Value of savings = $114550
Present Value of annuity = annual amount*(1-(1+rate)^(no. of years))/rate
=> 114550 = annual amount*(1-(1+10%)^(-25))/10%
=$12619.75
Hence, the amount is $12619.75
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