Bob and Sue are twins. Bob invests $10,000 at 8% at age 25. Sue invests $10,000 at 8% at age 30. Both of their investments compound annually, neither Bob nor Sue withdraw any of their principal or interest before retirement, and both of them retire at age 70. Which of the following statements is correct?
If both Bob and Sue wait to age 75 to retire they will have equal amounts of savings. |
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Sue will earn more interest on interest than Bob. |
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Sue will earn more compound interest than Bob. |
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Bob will have more money than Sue at any age. |
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Bob will have less money when he retires than Sue. |
Both Bob and Sue retire at age 75
Investment Amount = P = $10000
Interest rate = r = 8%
Number of years amount invested for Bob = n_{1} = 75 -
25 = 50 years
Value of amount at age 75 for Bob = P(1+r)^{n1}
= 10000(1+0.08)^{50} = $469016.13
Number of years amount invested for Sue = n_{2} = 75 -
30 = 45 years
Value of amount at age 75 for Bob = P(1+r)^{n2}
= 10000(1+0.08)^{45} = $319204.49
Since Bob has started investing earlier, "Bob will have more money than Sue at any age."
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