Question

You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is

$1,850

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 interest rate = 7.5% APR
That means monthly interest rate = 7.5% / 12 = 0.625%

Step 1: Find the loan amount.

We can use present value of annuity to find the answer:

Where,
PVA = Present value of annuity or loan amount
A = Annuity or monthly payment
i = Monthly Interest rate in decimal form
n = Number of payments

i = 0.625% or 0.00625
n = 30 * 12 = 360 payments

Substituting the values, we get:

Step 2: Find the balance of loan after 56 payments ..............( (4*12) + 8 = 56)

We have the formula:

Where,
PV = Original balance

and here n = 56

Therefore,

Therefore, today you owe  $251,465.14 on the mortgage loan.