Question

You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is $ 3 comma 120 and you have made every payment on time. The original term of the mortgage was 30​ years, and the mortgage is exactly four years and eight months old. You have just made your monthly payment. The mortgage interest rate is 7.500 % ​(APR). How much do you owe on the mortgage​ today?

Answer 1

Answer:

Mortgage liaiblity today: 424.092,31‬

Explanation:

We need to solve for mortage principal then;

how much do we amortize during four years and eight months old.

Last, decrease from the principal to know the current mortgage liability:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 3,120

time 360 (30 years x 12 months per year)

rate 0.00625

$3120 \times \frac{1-(1+0.00625)^{-360} }{0.00625} = PV$

PV $446,214.9972

Interest at first period:

446,215 x 0.00625 = 2.788,84

Amortization at first period:

3120 - 2,788.84 = 331.16

Total Amount amortized: will be the future value of the annuity of this first depreication during the life of the mortgage

$C \times \frac{(1+r)^{time} -1}{rate} = FV$

C 331

time 56

rate 0.00625

$331.16 \times \frac{(1+0.00625)^{56} -1}{0.00625} = FV$

Total Amortized: $22,122.6919

Mortgage liaiblity today:

446,215 - 22,122.69 = 424.092,31‬