Questions: On October 1, the home mortgage balance was 189,000 for the home owned by Susan Reed. The interest rate for the loan is 7.6 percent. Assuming that Susan makes the October monthly mortgage payment of 1890, calculate the following: (a) The amount of interest included in the October payment (round your answer to the nearest cent). (b) The amount of the monthly mortgage payment that will be used to reduce the principal balance. (c) The new balance after Susan makes this monthly mortgage payment. (a) Interest amount: (b) Principal reduction: (c) New balance:

Solution Steps

To solve this problem, we need to calculate the interest for the month, the principal reduction, and the new balance after the payment.

(a) Calculate the monthly interest by multiplying the annual interest rate by the principal balance and dividing by 12.

(b) Subtract the interest amount from the total monthly payment to find the principal reduction.

(c) Subtract the principal reduction from the original balance to find the new balance.

The monthly interest amount can be calculated using the formula: \[ \text{Interest Amount} = \text{Principal Balance} \times \left(\frac{\text{Annual Interest Rate}}{12}\right) \] Substituting the values: \[ \text{Interest Amount} = 189000 \times \left(\frac{0.076}{12}\right) = 1197.0 \]

The principal reduction is found by subtracting the interest amount from the total monthly payment: \[ \text{Principal Reduction} = \text{Monthly Payment} - \text{Interest Amount} \] Substituting the values: \[ \text{Principal Reduction} = 1890 - 1197.0 = 693.0 \]

The new balance after the payment is calculated by subtracting the principal reduction from the original principal balance: \[ \text{New Balance} = \text{Principal Balance} - \text{Principal Reduction} \] Substituting the values: \[ \text{New Balance} = 189000 - 693.0 = 188307.0 \]

Final Answer