Let's solve the problem step-by-step: Given: - Present Value (PV) = $520 - Future Value (FV) = $1,960.91 - Number of years (n) = 15 - Interest rate (r) = ? (compounded annually) The formula for compound interest is: \[ FV = PV \times (1 + r)^n \] Plug in the known values: \[ 1960.91 = 520 \times (1 + r)^{15} \] Divide both sides by 520: \[ \frac{1960.91}{520} = (1 + r)^{15} \] \[ 3.771 = (1 + r)^{15} \] Take the 15th root of both sides: \[ 1 + r = (3.771)^{1/15} \] Now, calculate: 1. **Find the 15th root of 3.771:** \[ (3.771)^{1/15} \] Use a calculator or logarithms: \[ \ln(3.771) \approx 1.327 \] \[ \frac{1.327}{15} \approx 0.08847 \] \[ e^{0.08847} \approx 1.0925 \] So, \[ 1 + r \approx 1.0925 \] 2. **Find r:** \[ r = 1.0925 - 1 = 0.0925 \] 3. **Convert to percentage:** \[ 0.0925 \times 100 = 9.25\% \] --- ### **Final Answer** The annual interest rate, compounded annually, at which $520 must be invested for it to grow to $1,960.91 in 15 years is: \[ \boxed{9.25\%} \] (Rounded to two decimal places.)