In this article we solve Question 4 of the compound interest quiz.

Question

On his 30th birthday, Bob wanted to start preparing for retirement on his 60th birthday by investing $10,000 a year at a rate of 10% per annum. On second thought, he realized that since he has so much time before retirement, he could delay starting the investment so that he now starts on his 40th birthday. In the first case, Bob would have invested for 30 years while in the second case he will only invest for 20 years. Thus, we would expect that the amount of money he will have after the 30-year investment will be more than the amount he will have after the 20-year investment. Which of the following best describes the relationship between the two investments?

A. The 20-year investment will yield a return that is about the same as what the 30-year investment will yield
B. The 20-year investment will yield a return that is about two-thirds of what the 30-year investment will yield
C. The 20-year investment will yield a return that is about one-half of what the 30-year investment will yield
D. The 20-year investment will yield a return that is about one-third of what the 30-year investment will yield
E. None of the above

Solution

Answer: D.