Final answer:
The rate of return on an investment earning 12 percent annually after 5 years is not a simple 60 percent due to the effect of compounding. The correct answer, using the assumption of the Rule of 72, is actually more than 60 percent but less than doubling – hence, the closest option given would be 72 percent.
Step-by-step explanation:
If an investment earns 12 percent annually, the rate of return after 5 years is not simply 12 percent multiplied by 5 years due to the effect of compounding. The formula for compound interest A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times interest is compounded per year, and t is the time the money is invested for in years.
In this scenario, the money is compounded once annually (n=1) for 5 years (t=5) at a 12 percent annual rate (r=0.12), so we apply the compound interest formula: A = 1000(1 + 0.12/1)^(1*5). Without the need to calculate the exact amount, we can already disqualify options 1, 2, and 4 as they assume simple interest rather than compound interest. By using the Rule of 72, which provides a rough estimate of the number of years required to double an investment with compound interest by dividing 72 by the annual rate of interest, we can see that an investment would double in 6 years at a 12% growth rate (72/12 = 6).
This implies that the correct answer is more than 60 percent but less than double in 5 years, leading to option 3) 72 percent, which is also supported by the fact that 12% compounded annually would be more than a simple accumulation of interest.