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

Mortgage liaiblity today: 424.092,31‬

Step-by-step 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 * (1-(1+r)^(-time) )/(rate) = PV\\`

C 3,120

time 360 (30 years x 12 months per year)

rate 0.00625

`3120 * (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 * ((1+r)^(time) -1)/(rate) = FV\\`

C 331

time 56

rate 0.00625

`331.16 * ((1+0.00625)^(56) -1)/(0.00625) = FV\\`

Total Amortized: $22,122.6919

Mortgage liaiblity today:

446,215 - 22,122.69 = 424.092,31‬