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Comparison of returns
Comparison of returns. WG Investors is looking at three different investment opportunities. Investment one is a five-year investment with a cost of $750 and a promised payout of $1,500 at maturity. Investment two is a seven-year investment with a cost of $750 and a promised payout of $2,100. Investment three is a ten-year investment with a cost of $750 and a promised payout of $3,600. WG Investors can take on only one of the three investments. Assuming that all three investment opportunities have the same level of risk, calculate the effective annual return for each investment, and select the best investment choice.
What is the effective annual return for investment one, a five-year investment with a cost of $750 and a promised payout of $1,500 at maturity? (Round to two decimal places.)
Expert Solution
| 1] | For investment one, we have the relationship: | |
| 1500 = 750*(1+r)^5, where, r = effective annual return. | ||
| Solving for r, | ||
| 1500/750 = (1+r)^5 | ||
| (1500/750)^(1/5) = 1+r | ||
| r = (1500/750)^(1/5)-1 | ||
| Thus, EAR for Investment one = (1500/750)^(1/5)-1 = | 14.87% | |
| Similarly for the other two investments: | ||
| EAR for Investment two = (2100/750)^(1/7)-1 = | 15.85% | |
| EAR for Investment three = (3600/750)^(1/10)-1 = | 16.98% | |
| 2] | As the EAR is the highest for Investment three, it is the | |
| best investment, |
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