1. **State the problem:** Benjamin invests 66000 at an interest rate of $6\frac{3}{8}\%$ compounded annually. Christian invests 66000 at an interest rate of $5\frac{3}{4}\%$ compounded continuously. We want to find how much more money Benjamin has than Christian after 19 years. 2. **Convert interest rates to decimals:** $6\frac{3}{8}\% = 6 + \frac{3}{8} = 6.375\% = 0.06375$ $5\frac{3}{4}\% = 5 + \frac{3}{4} = 5.75\% = 0.0575$ 3. **Formulas:** - Compound interest annually: $$A = P\left(1 + r\right)^t$$ - Continuous compounding: $$A = Pe^{rt}$$ where $P$ is principal, $r$ is rate, $t$ is time in years. 4. **Calculate Benjamin's amount:** $$A_B = 66000 \times \left(1 + 0.06375\right)^{19} = 66000 \times 1.06375^{19}$$ Calculate $1.06375^{19}$: $$1.06375^{19} \approx 3.1521$$ So, $$A_B = 66000 \times 3.1521 = 208038.6$$ 5. **Calculate Christian's amount:** $$A_C = 66000 \times e^{0.0575 \times 19} = 66000 \times e^{1.0925}$$ Calculate $e^{1.0925}$: $$e^{1.0925} \approx 2.9813$$ So, $$A_C = 66000 \times 2.9813 = 196765.8$$ 6. **Find the difference:** $$\text{Difference} = A_B - A_C = 208038.6 - 196765.8 = 11272.8$$ 7. **Final answer:** Benjamin would have approximately $11273$ more dollars than Christian after 19 years.