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

Respuesta :

Answer:

Option D ($1335) is the right answer.

Explanation:

  • Step 1:

[tex]PV=325000\times (1-25 \ percent)\\[/tex]

[tex]N=30\times 12\\[/tex]

[tex]\frac{I}{Y} =\frac{5.75 \ percent}{12} \\[/tex]

[tex]FV=0\\[/tex]

[tex]CPT \ PMT=$1,422.46\\[/tex]

  • Step 2:

[tex]PMT=1422.46[/tex]

[tex]PV=-325000\timse (1-25 \ percent)[/tex]

[tex]\frac{I}{Y} =\frac{5.75 \ percent}{12}[/tex]

[tex]N=12\times 5[/tex]

[tex]CPT \ FV=$226,107.75[/tex]

  • Step 3:

[tex]PV=-226107.75[/tex]

[tex]\frac{I}{Y} =\frac{5.1 \ percent}{12}[/tex]

[tex]N=12\times 25[/tex]

[tex]FV=0[/tex]

[tex]CPT \ PMT=$1,335.01[/tex]

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

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