1. **State the problem:** You want to find out how big of a loan you can afford if you can pay $400 per month for 3 years at 4% annual interest. 2. **Formula used:** The loan amount $P$ for an installment loan can be found using the formula for the present value of an annuity: $$P = \frac{PMT \times \left(1 - (1 + r)^{-n}\right)}{r}$$ where: - $PMT$ is the monthly payment - $r$ is the monthly interest rate (annual rate divided by 12) - $n$ is the total number of payments 3. **Calculate values:** - Annual interest rate = 4% = 0.04 - Monthly interest rate $r = \frac{0.04}{12} = 0.003333...$ - Number of payments $n = 3 \times 12 = 36$ - Monthly payment $PMT = 400$ 4. **Plug values into formula:** $$P = \frac{400 \times \left(1 - (1 + 0.003333)^{-36}\right)}{0.003333}$$ 5. **Calculate $(1 + r)^{-n}$:** $$ (1 + 0.003333)^{-36} = (1.003333)^{-36} \approx 0.8869 $$ 6. **Calculate numerator:** $$ 1 - 0.8869 = 0.1131 $$ 7. **Calculate loan amount:** $$P = \frac{400 \times 0.1131}{0.003333} = \frac{45.24}{0.003333} \approx 13572$$ 8. **Interpretation:** You can afford a loan of approximately $13572$ with a $400 monthly payment over 3 years at 4% interest. **Final answer:** $$\boxed{13572}$$