To check the Rule of 72, let's calculate the future value of $100 invested at the given interest rates and periods of time.

Formula for compound interest:

The compound interest formula is:

$A = P \times \left(1 + \frac{r}{100}\right)^t$

Where:

• $A$ = Future Value (amount of money accumulated)
• $P$ = Principal amount (initial investment)
• $r$ = Interest rate (annual)
• $t$ = Time (in years)

Now, let's calculate the two scenarios.

(a) $100 invested at 6% interest for 12 years

Given:

• $P = 100$
• $r = 6\%$
• $t = 12$ years

Using the compound interest formula, the future value $A$ is:

= 100 \times (1.06)^{12}$$ ### (b) $100 invested at 4% interest for 18 years Given: - $$P = 100$$ - $$r = 4\%$$ - $$t = 18$$ years Using the same formula, the future value $$A$$ is: $$A = 100 \times \left(1 + \frac{4}{100}\right)^{18} = 100 \times (1.04)^{18}$$ Let's compute both values.Here are the results: ### (a) $100 invested at 6% interest for 12 years: - The future value is approximately **$201.22**. ### (b) $100 invested at 4% interest for 18 years: - The future value is approximately **$202.58**. In both cases, the investment nearly doubled, as predicted by the Rule of 72. The Rule of 72 is a good approximation for estimating the doubling time. Would you like more details or explanations on this? Here are some related questions: 1. How does the Rule of 72 work for different interest rates? 2. What are the limitations of the Rule of 72 for high interest rates? 3. How does the compounding frequency (e.g., monthly vs annually) affect the result? 4. Can the Rule of 72 be applied to inflation or debt calculations? 5. What happens when interest is compounded more frequently than annually? **Tip:** The Rule of 72 works best for interest rates between 6% and 10%. For rates far outside this range, the accuracy diminishes slightly.