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February 24th, 2015, 01:52 PM   #1
Joined: Feb 2015
From: Sylmar

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Power of compounding

a. You borrowed \$1,000 from a loan shark at 5% monthly interest. How much do you owe four years later?
b. You are trying to build a nest egg for your retirement. You have estimated that you will need income of \$5,000 a month in order to live comfortably after retirement. How large a nest egg (principal P_{0}) must you have at retirement? Assume that at your retirement you put that money, P_{0}, in an annuity with a guaranteed annual return of 8%. And suppose you think you will live forever.
c. You are now 25 and plan to retire at age 65. You want to start saving so that you can build a nest egg of \$1 million. How much should you save each month? Assume that your savings will be earning 10% interest each year, compounded monthly.

Last edited by skipjack; February 24th, 2015 at 04:37 PM.
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February 24th, 2015, 05:05 PM   #2
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(a). \$1,000 × $1.05^{48}$ = \$10,401.27 approximately. The amount owed will be slightly higher if the monthly interest is always rounded to the nearest \$0.01, and slightly lower if the monthly interest is always rounded down.
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