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?
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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 \( \$154,212.84 \).