You can afford a \( \$ 800 \) per month mortgage payment. You've found a 30 year loan at \( 6 \% \) interest. a) How big of a loan can you afford? b) How much total money will you pay the loan company? c) How much of that money is interest?

To figure this out, we can use the formula for a fixed-rate mortgage: \[ M = P \frac{r(1+r)^n}{(1+r)^n - 1} \] where \( M \) is the monthly payment, \( P \) is the loan amount, \( r \) is the monthly interest rate, and \( n \) is the number of payments. Given \( M = 800 \), \( r = \frac{0.06}{12} = 0.005 \), and \( n = 30 \times 12 = 360 \): a) Plugging these into the formula, we can rearrange to find \( P \): \[ P = \frac{M \cdot \left((1+r)^n - 1\right)}{r(1+r)^n} \] After calculating, you would find \( P \) (the loan amount you can afford) to be approximately \( \$133,787.16 \). b) Total payments over 30 years is: \[ \text{Total Payments} = M \times n = 800 \times 360 = \$288,000. \] c) The interest paid over the life of the loan is: \[ \text{Interest} = \text{Total Payments} - P = 288,000 - 133,787.16 = \$154,212.84. \] So in summary: - You can afford a loan of approximately \( \$133,787.16 \). - You will pay a total of \( \$288,000 \) to the loan company. - The interest paid will be approximately \( \$154,212.84 \).