Calculate the interest rate that a company would be charged if they promised to quintuple their money in 7 years and 4 months.

1. Rewrite the equation for quintupling using \(PV\) and \(FV\):

5 = (1 + r)^{\frac{22}{3}}

2. Take the natural log on both sides:

\ln(5) = \frac{22}{3} \ln(1 + r)

3. Rearrange for \(\ln(1 + r)\):

\ln(1 + r) = \frac{3 \ln(5)}{22}

4. Exponentiate to find \(1 + r\):

1 + r = e^{\frac{3 \ln(5)}{22}}

5. Solve for \(r\):

r = e^{\frac{3 \ln(5)}{22}} - 1

6. Calculate \(r\):

r\approx0.2454\text{ or }24.54\%

Thus, the interest rate is approximately 24.54%.