1. **State the problem:** You want to find the maximum loan amount you can afford with a monthly payment of 200, a loan term of 3 years, and an annual interest rate of 5%. 2. **Formula used:** The loan payment formula for an installment loan is $$P = \frac{r \times L}{1 - (1 + r)^{-n}}$$ where: - $P$ is the monthly payment, - $L$ is the loan amount (what we want to find), - $r$ is the monthly interest rate (annual rate divided by 12), - $n$ is the total number of payments (months). 3. **Calculate values:** - Annual interest rate = 5% = 0.05 - Monthly interest rate $r = \frac{0.05}{12} = 0.0041667$ - Number of payments $n = 3 \times 12 = 36$ - Monthly payment $P = 200$ 4. **Rearrange formula to solve for $L$:** $$L = \frac{P \times (1 - (1 + r)^{-n})}{r}$$ 5. **Calculate intermediate values:** - Calculate $(1 + r)^{-n} = (1 + 0.0041667)^{-36} = 1.0041667^{-36}$ - Using a calculator, $1.0041667^{36} \approx 1.1616$, so $$1.0041667^{-36} = \frac{1}{1.1616} \approx 0.8607$$ 6. **Calculate $L$:** $$L = \frac{200 \times (1 - 0.8607)}{0.0041667} = \frac{200 \times 0.1393}{0.0041667} = \frac{27.86}{0.0041667} \approx 6686.4$$ **Final answer:** You can afford a loan of approximately $6686.40$ with a $200 monthly payment over 3 years at 5% interest.