1. **Problem Statement:** You have won 50000 and want to invest it for 30 years. You have two options: - Money market with 8.5% interest compounded quarterly. - Savings account with 7.9% interest compounded continuously. Which option yields more money? 2. **Formulas:** - For quarterly compounding, the amount after time $t$ is given by: $$A = P\left(1 + \frac{r}{n}\right)^{nt}$$ where $P$ is principal, $r$ is annual interest rate (decimal), $n$ is number of compounding periods per year, and $t$ is years. - For continuous compounding, the amount is: $$A = Pe^{rt}$$ 3. **Calculate for quarterly compounding:** Given $P=50000$, $r=0.085$, $n=4$, $t=30$: $$A = 50000\left(1 + \frac{0.085}{4}\right)^{4 \times 30} = 50000\left(1 + 0.02125\right)^{120} = 50000(1.02125)^{120}$$ Calculate $(1.02125)^{120}$: Using a calculator, $(1.02125)^{120} \approx 8.252$. So, $$A \approx 50000 \times 8.252 = 412600$$ 4. **Calculate for continuous compounding:** Given $P=50000$, $r=0.079$, $t=30$: $$A = 50000 e^{0.079 \times 30} = 50000 e^{2.37}$$ Calculate $e^{2.37}$: Using a calculator, $e^{2.37} \approx 10.7$. So, $$A \approx 50000 \times 10.7 = 535000$$ 5. **Conclusion:** The savings account with continuous compounding yields approximately 535000, which is more than the 412600 from quarterly compounding. **Therefore, choose the savings account with continuous compounding for a better return.**