1. **State the problem:** We need to find the number of years $t$ for a principal amount $P=5000$ to grow to a final amount $A=20000$ at an annual compound interest rate $r=5.5\% = 0.055$. 2. **Formula used:** The compound interest formula is $$A = P \left(1 + r\right)^t$$ where $A$ is the amount after $t$ years, $P$ is the principal, $r$ is the annual interest rate, and $t$ is the time in years. 3. **Substitute known values:** $$20000 = 5000 \left(1 + 0.055\right)^t$$ 4. **Simplify inside the parentheses:** $$20000 = 5000 \times 1.055^t$$ 5. **Divide both sides by 5000:** $$\frac{20000}{5000} = \cancel{\frac{5000}{5000}} \times 1.055^t$$ $$4 = 1.055^t$$ 6. **Take natural logarithm on both sides to solve for $t$:** $$\ln(4) = \ln\left(1.055^t\right)$$ 7. **Use logarithm power rule:** $$\ln(4) = t \ln(1.055)$$ 8. **Solve for $t$:** $$t = \frac{\ln(4)}{\ln(1.055)}$$ 9. **Calculate values:** $$\ln(4) \approx 1.3863, \quad \ln(1.055) \approx 0.0536$$ 10. **Final calculation:** $$t \approx \frac{1.3863}{0.0536} \approx 25.86$$ **Answer:** It will take approximately **26 years** for the sum to grow from 5000 to 20000 at 5.5% compound interest annually.