1. **State the problem:** You can afford monthly payments of 600. The mortgage rate is 2.41% annually for a 15-year fixed loan. We want to find how much you can borrow (the loan principal $P$). 2. **Formula used:** 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 interest rate = 2.41% = 0.0241 - Monthly interest rate $r = \frac{0.0241}{12} = 0.002008333...$ - Loan term = 15 years = $15 \times 12 = 180$ months 4. **Rearrange formula to solve for $P$:** $$P = M \times \frac{(1+r)^n - 1}{r(1+r)^n}$$ 5. **Calculate $(1+r)^n$:** $$ (1+0.002008333)^{180} = 1.002008333^{180} \approx 1.4116 $$ 6. **Substitute values:** $$P = 600 \times \frac{1.4116 - 1}{0.002008333 \times 1.4116} = 600 \times \frac{0.4116}{0.002835}$$ 7. **Simplify:** $$P = 600 \times 145.13 = 87078$$ So, you can afford to borrow approximately **87078**. 8. **Calculate the maximum home price with 20% down payment:** If $P$ is 80% of the home price $H$, then $$H = \frac{P}{0.8} = \frac{87078}{0.8} = 108848$$ **Final answers:** - Amount you can borrow: **87078** - Maximum home price you can afford: **108848**