Questions: You can afford a 1050 per month mortgage payment. You've found a 30 year loan at an annual interest rate of 4.3%, compounded monthly. (Enter numeric answers to 2 decimal places.) 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? You want to buy a 270,000.00 home. You plan to pay 10% as a down payment, and take out a 25-year loan for the rest.

Solution Steps

To solve the first question, we need to determine the maximum loan amount you can afford given a monthly mortgage payment, interest rate, and loan term. This involves using the formula for the monthly payment of an amortizing loan, which is derived from the present value of an annuity formula. Once we have the loan amount, we can calculate the total amount paid over the life of the loan by multiplying the monthly payment by the number of payments. The interest paid is the total amount paid minus the principal (loan amount).

To determine the maximum loan amount \( L \) that can be afforded with a monthly payment \( P \), we use the formula for the present value of an annuity:

\[ L = P \cdot \frac{1 - (1 + r)^{-n}}{r} \]

where:

• \( P = 1050 \)
• \( r = \frac{0.043}{12} = 0.0035833333 \)
• \( n = 30 \times 12 = 360 \)

Substituting the values, we find:

\[ L = 1050 \cdot \frac{1 - (1 + 0.0035833333)^{-360}}{0.0035833333} \approx 212176.32 \]

The total amount paid \( T \) over the life of the loan is given by:

\[ T = P \cdot n \]

Substituting the values:

\[ T = 1050 \cdot 360 = 378000 \]

The total interest paid \( I \) is calculated as:

\[ I = T - L \]

Substituting the values:

\[ I = 378000 - 212176.32 \approx 165823.68 \]

Final Answer