SOLUTION: The Hayes family recently purchased a home. They borrowed $330,000 at 8.99% for 30 years (360 payments). Their monthly payment (excluding insurance and taxes) is $2,652.88. How muc

Question 1032539: The Hayes family recently purchased a home. They borrowed $330,000 at 8.99% for 30 years (360 payments). Their monthly payment (excluding insurance and taxes) is $2,652.88. How much of their first payment is applied to principal?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the monthly interest rate is equal to 8.99% / 1200 = .0074916667.

330,000 is multiplied by the monthly interest rate to get the interest charged for the first month.

the interest is subtracted from the monthly payment to get the amount of the loan payment that is applied to the principal.

that is used to reduce the remaining balance of the loan.

for the first month, the interest charged is .0074916667 * 330,000 = 2472.15

subtract that from 2652.88 and you get the principal part of the payment = 180.63

that's the part that's used to reduce the remaining balance of the loan.

here's two pictures of my excel worksheet showing the first few months of the loan and the last few months of the loan.

a couple of the calculations will be shown below the pictures.

the titles of the columns are:

tp = time point
rembal = remaining balance of the loan.
pmt = monthly payment on the loan.
int = part of the payment applied to paying off the interest.
princ = principal part of the payment applied to reducing the remaining balance of the loan.

in time point 0, the remaining balance on the loan is 330,000.

in time point 1, the following happens:

330,000 is multiplied by .0074916667 to get the interest charge of 2472.25.
the difference between the monthly payment of 2652.88 and the interest charge of 2472.25 is the principal part of the loan payment equal to 180.63 that is subtracted from 330,000 to get a new remaining balance of $329,819.37.

these calculations can be seen in the first picture shown below:

in time point 359, the remaining balance on the loan is $2,633.15.

in time point 360, the following happens:

$2,633.15 is multiplied by .0074916667 to get the interest charge of $19.73.
the difference between the monthly payment of 2652.88 and the interest charge of $19.73 is the principal part of the loan payment equal to $2,633.15 that is subtracted from $2,633.15 to get a new remaining balance of $0.00.

these calculations can be seen in the second picture shown below:

as the loan matures, the part of the payment that is applied to the interest gets less and the part of the loan that is applied to the principal gets more.

Answer by MathTherapy(10549) (Show Source): You can put this solution on YOUR website!

The Hayes family recently purchased a home. They borrowed $330,000 at 8.99% for 30 years (360 payments). Their monthly payment (excluding insurance and taxes) is $2,652.88. How much of their first payment is applied to principal?

The $2,652.88 monthly payment (PMT) is a combination of the amount that's applied to interest (SI), and the amount applied to principal (P)
Therefore, we have: PMT = SI + P --------> P = PMT - SI
P = PMT - PTR ------- Substituting PTR for SI

P, or amount applied to principal (P) =
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