You can afford a \( \$ 1400 \) per month mortgage payment. You've found a 30 year loan at \( 8 \% \) interest. a) How big of a loan can you afford? Round your answer to the nearest dollar. b) How much total money will you pay the loan company? Round your answer to the nearest dollar. c) How much of that money is interest? Round your answer to the nearest dollar.

To find out how big of a loan you can afford with a monthly mortgage payment of \( \$1400 \) at an \( 8\% \) interest rate over 30 years, you can use the formula for monthly mortgage payments: \[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \] where: - \( M \) is the monthly payment (\$1400), - \( P \) is the loan amount, - \( r \) is the monthly interest rate (annual rate / 12), - \( n \) is the number of payments (30 years \(\times\) 12 months/year = 360). First, calculate the monthly interest rate: \[ r = \frac{0.08}{12} \approx 0.0066667 \] Now, plug in the values into the formula rearranged to find \( P \): \[ P \approx M \frac{(1 + r)^n - 1}{r(1 + r)^n} \approx 1400 \frac{(1 + 0.0066667)^{360} - 1}{0.0066667(1 + 0.0066667)^{360}} \] Calculating \( P \): \[ P \approx 1400 \frac{(1.0066667)^{360} - 1}{0.0066667(1.0066667)^{360}} \approx 1400 \cdot 133.4802 \approx 186872 \] Thus, the loan amount you can afford is approximately **$186,872**. **Total Money Paid to the Loan Company:** To find out the total money paid to the loan company, multiply the monthly payment by the total number of payments. \[ \text{Total Paid} = M \cdot n = 1400 \cdot 360 = 504000 \] So, the total money you will pay the loan company is **$504,000**. **Total Interest Paid:** Finally, to calculate the total interest paid over the life of the loan, subtract the original loan amount from the total paid: \[ \text{Total Interest} = \text{Total Paid} - P = 504000 - 186872 = 317128 \] Thus, the amount of money that goes towards interest is approximately **$317,128**.