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Jala put [tex]\[tex]$600[/tex] in an interest-bearing account with an annual compound interest rate of [tex]5\%[/tex]. Jala determined that after seven years, she will have a total balance of [tex]\$[/tex]844.26[/tex].
Using the rule of 72, [tex]t=\frac{72}{r}[/tex], how many more years will it be before Jala's [tex]\$600[/tex] doubles in value? Round to the nearest tenth.
A. 3.3 years B. 7.4 years C. 10.3 years D. 14.4 years
To determine how many more years it will take for Jala's \[tex]$600 to double using the rule of 72, we can follow these steps:
1. Understand the Rule of 72: The rule of 72 is a simplified way to estimate the number of years required to double an investment at a fixed annual rate of interest. The formula is:
\[
t = \frac{72}{r}
\]
where \( t \) is the number of years and \( r \) is the annual interest rate.
2. Given Values:
- Initial principal (\( P \)) = \$[/tex]600 - Annual interest rate ([tex]\( r \)[/tex]) = 5% - The rule of 72 will help us determine the time to double the investment.
3. Apply the Rule of 72: - Here, [tex]\( r = 5 \)[/tex]. [tex]\[
t = \frac{72}{5}
\][/tex]
4. Calculate the Time to Double: - Compute the quotient: [tex]\[
t = \frac{72}{5} = 14.4 \text{ years}
\][/tex]
5. Conclusion: - It takes approximately 14.4 years for Jala's \$600 to double in value at a 5% annual interest rate using the rule of 72.
Thus, among the options provided:
A) 3.3 years B) 7.4 years C) 10.3 years D) 14.4 years
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