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 = \( \frac{100}{\text{Interest Rate (\%)} } \)

Answer: (A)

Verified step by step guidance

1. 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.
2. 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 = \( \frac{72}{\text{Interest Rate (\%)} } \).
3. 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.
4. 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.
5. 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.