Question

You purchase a $325,000 town home and you pay 25% down. You obtain a 30-year fixed-rate mortgage with an annual interest rate of 5.75%. After 5 years you refinance the mortgage for 25 years at a 5.1% annual interest rate. After you refinance, what is the new monthly payment (to the nearest dollar)?

A. $1,422
B. $1,401
C. $1,366
D. $1,335
E. $1,296

Answer 1

The new monthly payment after refinancing is $1,366.

Step-by-step explanation:

To find the new monthly payment after refinancing, we first need to calculate the remaining loan amount after 5 years. Since the down payment was 25%, the initial loan amount is 75% of $325,000, which is $243,750. After 5 years, we need to calculate the loan balance using the formula:

Loan Balance = Initial Loan Amount * (1 + Monthly Interest Rate)^(Number of Payments)

Where the Monthly Interest Rate is (Annual Interest Rate / 12) and the Number of Payments is (Number of Years * 12). The monthly interest rate after refinancing is 5.1% / 12 = 0.425% and the number of payments is (25 * 12) = 300. Plugging these values into the formula:

Loan Balance = $243,750 * (1 + 0.00425)^300 = $198,915.51

Finally, we can calculate the new monthly payment using the formula for a fixed-rate mortgage:

New Monthly Payment = (Loan Balance * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))

Plugging in the values:

New Monthly Payment = ($198,915.51 * 0.00425) / (1 - (1 + 0.00425)^(-300)) = $1,366

Therefore, the new monthly payment after refinancing is $1,366.

Answer 2

Option D ($1335) is the right answer.

Step-by-step explanation:

• Step 1:

`PV=325000* (1-25 \ percent)\\`

`N=30* 12\\`

`(I)/(Y) =(5.75 \ percent)/(12) \\`

`FV=0\\`

`CPT \ PMT=$1,422.46\\`

• Step 2:

`PMT=1422.46`

`PV=-325000\timse (1-25 \ percent)`

`(I)/(Y) =(5.75 \ percent)/(12)`

`N=12* 5`

`CPT \ FV=$226,107.75`

• Step 3:

`PV=-226107.75`

`(I)/(Y) =(5.1 \ percent)/(12)`

`N=12* 25`

`FV=0`

`CPT \ PMT=$1,335.01`

The other options offered aren't really relevant to the scenario presented. So, the solution here is just the right one.