Answered

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



Answer :

GinnyAnswer
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

The correct answer is 14.4 years.

Other Questions