QuestionOn February 1, the home mortgage balance was $\$ 129,000$ for the home owned by Tom Bryant. The interest rate for the loan is 7 percent. Assuming that Tom makes the February monthly mortgage payment of $\$ 1032$ , calculate the following: (a) The amount of interest included in the February 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 Tom makes this monthly mortgage payment.

Studdy Solution

STEP 1

1. The home mortgage balance on February 1 is $129,000.<br />2. The annual interest rate for the loan is 7%.<br />3. The monthly mortgage payment made by Tom is$ 1,032.
4. We need to calculate: - (a) The amount of interest included in the February payment. - (b) The amount of the monthly mortgage payment used to reduce the principal balance. - (c) The new balance after the monthly mortgage payment.

STEP 2

1. Calculate the monthly interest amount.
2. Determine the amount of the payment that reduces the principal.
3. Calculate the new balance after the payment.

STEP 3

Calculate the monthly interest amount.
The monthly interest rate is the annual rate divided by 12: $\text{Monthly interest rate} = \frac{7\%}{12} = \frac{0.07}{12}$
Calculate the interest for February: $\text{Interest for February} = \text{Mortgage balance} \times \text{Monthly interest rate}$ $\text{Interest for February} = 129,000 \times \frac{0.07}{12}$
Calculate the value: $\text{Interest for February} = 129,000 \times 0.0058333$ $\text{Interest for February} = 752.50$
(a) The amount of interest included in the February payment is $\boxed{752.50}$ .

STEP 4

Determine the amount of the payment that reduces the principal.
Subtract the interest from the total payment to find the amount reducing the principal: $\text{Principal reduction} = \text{Monthly payment} - \text{Interest for February}$ $\text{Principal reduction} = 1,032 - 752.50$ $\text{Principal reduction} = 279.50$
(b) The amount of the monthly mortgage payment that will be used to reduce the principal balance is $\boxed{279.50}$ .

STEP 5

Calculate the new balance after the payment.
Subtract the principal reduction from the original balance: $\text{New balance} = \text{Original balance} - \text{Principal reduction}$ $\text{New balance} = 129,000 - 279.50$ $\text{New balance} = 128,720.50$
(c) The new balance after Tom makes this monthly mortgage payment is $\boxed{128,720.50}$ .

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