Questions: You can afford a 1250 per month mortgage payment. You've found a 30 year loan at 8% 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?

Solution Steps

To solve this problem, we need to calculate the loan amount you can afford based on a monthly mortgage payment, the total amount paid over the life of the loan, and the total interest paid.

1. Loan Amount Calculation: Use the formula for the present value of an annuity to determine the loan amount.
2. Total Payment Calculation: Multiply the monthly payment by the total number of payments (months).
3. Interest Calculation: Subtract the loan amount from the total payment to find the total interest paid.

To determine the maximum loan amount you can afford with a monthly payment of \( \$1250 \), we use the present value of an annuity formula:

\[ PV = PMT \times \frac{1 - (1 + r)^{-n}}{r} \]

where:

• \( PV \) is the present value (loan amount),
• \( PMT = 1250 \) is the monthly payment,
• \( r = \frac{0.08}{12} = 0.00666667 \) is the monthly interest rate,
• \( n = 30 \times 12 = 360 \) is the total number of payments.

Substituting the values, we find:

\[ PV = 1250 \times \frac{1 - (1 + 0.00666667)^{-360}}{0.00666667} \approx 170354.37 \]

The total amount paid over the life of the loan is calculated as:

\[ \text{Total Payment} = PMT \times n = 1250 \times 360 = 450000 \]

The total interest paid over the life of the loan is given by:

\[ \text{Total Interest} = \text{Total Payment} - PV = 450000 - 170354.37 \approx 279645.63 \]

Final Answer