Multiple Choice
If \$1 is compounded semiannually for 5 years at an annual interest rate of 2%, how many compounding periods will there be in total?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
Which one of the following formulas correctly defines the Rule of 72 for estimating the number of years required to double an investment at a given annual interest rate?
A
Years to double = \( \frac{72}{\text{Interest Rate (\%)} } \)
B
Years to double = \( \frac{\text{Interest Rate (\%)}}{72} \)
C
Years to double = \( 72 \times \text{Interest Rate (\%)} \)
D
Years to double = \( \frac{100}{\text{Interest Rate (\%)} } \)
Verified step by step guidance1
Step 1: Understand the Rule of 72. It is a simple formula used to estimate the number of years required to double an investment at a given annual interest rate. The formula is based on the principle of compounding interest.
Step 2: Identify the correct formula from the options provided. The Rule of 72 states that the number of years to double an investment is calculated as: Years to double = \( \frac{72}{\text{Interest Rate (\%)} } \).
Step 3: Analyze why the other formulas are incorrect. For example, \( \frac{\text{Interest Rate (\%)}}{72} \) does not align with the Rule of 72, as it reverses the relationship between the interest rate and the years to double. Similarly, \( 72 \times \text{Interest Rate (\%)} \) and \( \frac{100}{\text{Interest Rate (\%)}} \) do not follow the established formula for estimating doubling time.
Step 4: Apply the correct formula to a hypothetical scenario. For instance, if the annual interest rate is 6%, the formula \( \frac{72}{\text{Interest Rate (\%)}} \) would be used to calculate the approximate number of years to double the investment.
Step 5: Remember that the Rule of 72 is an approximation and works best for interest rates between 6% and 10%. For very high or very low interest rates, the accuracy of the formula may decrease.
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