1. **State the problem:** You can afford monthly payments of 800. The mortgage rate is 4.04% annually for a 30-year fixed loan. We want to find how much you can borrow (the loan principal $P$). 2. **Formula:** The loan payment formula is $$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$ where: - $M$ is the monthly payment, - $P$ is the loan principal (amount borrowed), - $r$ is the monthly interest rate (annual rate divided by 12), - $n$ is the total number of payments (months). 3. **Calculate parameters:** - Annual rate = 4.04% = 0.0404 - Monthly rate $r = \frac{0.0404}{12} = 0.0033667$ - Number of payments $n = 30 \times 12 = 360$ 4. **Rearrange formula to solve for $P$:** $$P = M \times \frac{(1+r)^n - 1}{r(1+r)^n}$$ 5. **Calculate $(1+r)^n$:** $$ (1+0.0033667)^{360} = 3.313$$ 6. **Substitute values:** $$P = 800 \times \frac{3.313 - 1}{0.0033667 \times 3.313} = 800 \times \frac{2.313}{0.01115}$$ 7. **Simplify:** $$P = 800 \times 207.56 = 166048$$ So, you can afford to borrow approximately **166048**. 8. **Calculate home price with 10% down payment:** If $P$ is 90% of the home price $H$, then $$H = \frac{P}{0.9} = \frac{166048}{0.9} = 184498$$ **Final answers:** - Loan amount you can afford: **166048** - Maximum home price you can afford: **184498**