Questions: The total interest that would be paid on the 35-year loan with a 23% down payment is .

Solution Steps

To find the total interest paid on a 35-year loan with a 23% down payment, we need to calculate the loan amount after the down payment and then determine the total interest over the loan period. The total interest can be calculated by subtracting the principal from the total amount paid over the loan term.

The down payment is calculated as follows: \[ \text{Down Payment} = \text{Total Cost} \times \left(\frac{\text{Down Payment Percentage}}{100}\right) = 1000000 \times \left(\frac{23}{100}\right) = 230000 \]

The loan amount after the down payment is: \[ \text{Loan Amount} = \text{Total Cost} - \text{Down Payment} = 1000000 - 230000 = 770000 \]

The monthly interest rate and the number of payments are: \[ \text{Monthly Interest Rate} = \frac{\text{Annual Interest Rate}}{12} = \frac{0.05}{12} \approx 0.0041667 \] \[ \text{Number of Payments} = \text{Loan Term in Years} \times 12 = 35 \times 12 = 420 \] The monthly payment is calculated using the formula for an annuity: \[ \text{Monthly Payment} = \text{Loan Amount} \times \frac{\text{Monthly Interest Rate} \times (1 + \text{Monthly Interest Rate})^{\text{Number of Payments}}}{(1 + \text{Monthly Interest Rate})^{\text{Number of Payments}} - 1} \] Substituting the values: \[ \text{Monthly Payment} \approx 770000 \times \frac{0.0041667 \times (1 + 0.0041667)^{420}}{(1 + 0.0041667)^{420} - 1} \approx 3886.0951 \]

The total amount paid over the loan term is: \[ \text{Total Paid} = \text{Monthly Payment} \times \text{Number of Payments} = 3886.0951 \times 420 \approx 1632159.9386 \]

The total interest paid is: \[ \text{Total Interest Paid} = \text{Total Paid} - \text{Loan Amount} = 1632159.9386 - 770000 \approx 862159.9386 \]

Final Answer