1. **State the problem:** A person borrows 5000 for 3 years with an interest rate of 10% per year compounded continuously. The loan is to be repaid in 36 equal monthly installments. We need to find the monthly payment amount. 2. **Formula and explanation:** For continuous compounding, the amount owed after time $t$ years is given by $$A = P e^{rt}$$ where $P$ is the principal, $r$ is the annual interest rate, and $t$ is time in years. 3. However, since the loan is repaid in equal monthly installments over 3 years (36 months), we use the formula for the monthly payment $M$ of a loan with continuous compounding interest: $$M = \frac{P r}{1 - e^{-rT}}$$ where $T$ is the total time in years (3 years), and $r$ is the annual interest rate (0.10). 4. **Calculate the monthly interest rate equivalent:** Since payments are monthly, the effective monthly rate under continuous compounding is $$r_m = \frac{r}{12} = \frac{0.10}{12} = 0.0083333$$ 5. **Calculate the denominator:** $$1 - e^{-r T} = 1 - e^{-0.10 \times 3} = 1 - e^{-0.3}$$ Calculate $e^{-0.3} \approx 0.740818$ so $$1 - 0.740818 = 0.259182$$ 6. **Calculate the monthly payment:** $$M = \frac{5000 \times 0.10}{12 \times 0.259182} = \frac{500}{0.259182} \approx 1928.75$$ 7. **Interpretation:** The monthly payment is approximately 1928.75. **Note:** This formula assumes continuous compounding but equal monthly payments, which is a simplification. More precise amortization with continuous compounding would require integral calculus or numerical methods. **Final answer:** The monthly payment is approximately $1928.75$.