Question

You're trying to choose between two investments of similar risk, both of which require an investment of $86,000 today. Investment G will be worth $151,000 in 7 years. Investment H will be worth $271,000 in 14 years. Which investment would you prefer? ESSENTIAL explain or show why the correct answer is correct AND why the other answers are not correct.

a. Investment G, since it has a shorter time horizon.
b. Investment H, because it has a higher rate of return.
c. Investment H, because it has a larger future value

Answer 1

To determine which investment is preferable, we need to calculate the rate of return for each investment. Investment G has a higher rate of return compared to Investment H, making it the preferred investment. Hence, the correct answer is option (a).

Step-by-step explanation:

When deciding between two investments of similar risk, it is important to calculate the rate of return for each to make an informed decision. For Investment G, which turns $86,000 into $151,000 over 7 years, we can use the future value formula or an average annual growth rate calculation to assess its performance. Similarly, with Investment H growing to $271,000 over 14 years, we must compute its return as well.

Let's calculate the compound annual growth rate (CAGR) for both investments:

For Investment G:
CAGR = [(151,000 / 86,000)^(1/7) - 1] = approximately 0.096 or 9.6%

For Investment H:
CAGR = [(271,000 / 86,000)^(1/14) - 1] = approximately 0.085 or 8.5%

Comparing the CAGRs, Investment G has a higher rate of return than Investment H even though the future value of H is larger. Hence, the better investment would be Investment G, not because it has a shorter time horizon as option (a) suggests, but because it yields a higher return. Investment H does have a higher future value but has a lower rate of return when considering the time value of money, making it less attractive.