3. Sailor Sam needs to have $15,000 at the end of 5 years to fulfill his dream o

Question

3. Sailor Sam needs to have $15,000 at the end of 5 years to fulfill his dream of buying a small sailboat. He is willing to invest the funds as a single amount today, but wonders what rate of investment return he will need to earn, depending on how much he has to invest. a. What is the approximate annual rate of return, compounded annually, needed if Sam can invest $10,200 today? b. What is the approximate annual rate of return, compounded annually, needed if Sam can invest $8,150 today? c. What is the approximate annual rate of return, compounded annually, needed if Sam can invest $7,150 today?

Explanation / Answer

Details Duration of investment =5 years Assume the required rate of return=r Compounding factor for 5 years=(1+r)^5 Required maturity amount =15000 a when the investment is 10,200 assume the required rate of return=r so, 10200(1+r)^5=15000 (1+r)^5=15000/10200=1.4706 r=8.02% so required return in this case =8.02% b when the investment is 8150 assume the required rate of return=r so, 8150(1+r)^5=15000 (1+r)^5=15000/8150= r=12.98% so required return in this case =12.98% c when the investment is 7150 assume the required rate of return=r so, 7150(1+r)^5=15000 (1+r)^5=15000/7150= r=15.97% so required return in this case =15.97%

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