Question
Double your money-Rule of 72. Approximately how long will it take to double your money if you get an annual return of \( 4.6 \%, 6.5 \% \), or \( 10.4 \% \) on your investment? Approximately how long will it take to double your money if you get a \( 4.6 \% \) annual return on your investment? years (Round to two decimal places.)
Ask by Patel Ray. in the United States
Jan 22,2025
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Tutor-Verified Answer
Answer
It will take approximately 15.65 years to double your money with a 4.6% annual return.
Solution
To estimate how long it will take to double your money using the **Rule of 72**, you can use the following formula:
\[
\text{Years to Double} = \frac{72}{\text{Annual Return (\%)}}
\]
### For a **4.6%** Annual Return:
\[
\text{Years to Double} = \frac{72}{4.6} \approx 15.65 \text{ years}
\]
**Therefore, it will take approximately 15.65 years to double your money with a 4.6% annual return.**
### Additional Calculations for Other Rates:
- **6.5% Annual Return:**
\[
\frac{72}{6.5} \approx 11.08 \text{ years}
\]
- **10.4% Annual Return:**
\[
\frac{72}{10.4} \approx 6.92 \text{ years}
\]
These estimates provide a quick way to gauge the growth of your investment over time using the Rule of 72.
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Bonus Knowledge
To estimate how long it will take to double your money using the Rule of 72, you simply divide 72 by your annual return percentage. For a \( 4.6\% \) return, it would take approximately \( 72 / 4.6 \approx 15.65 \) years to double your investment. At a \( 6.5\% \) annual return, you'd divide \( 72 / 6.5 \approx 11.08 \) years. And for a \( 10.4\% \) return, the calculation gives you \( 72 / 10.4 \approx 6.92 \) years. So, the magic of compounding really shines at higher rates!