Aborrower receives a mortgage for a 30 year loan with a principal balance of $225,000, a payment of $1245, and at an interest rate of 4.25%. if she makes 2 payments on the loan, what will her principal balance be after the second payment is applied?

$224,149

Explanation:

A mortgage is a long-term loan for the purpose of financing a house property acquisition. It is usually secured on the property to be financed .

The loan repayment is structured  such that a series of equal periodic installments will be paid for certain number of periods to offset both the loan and the accrued interest. This is called amortization.

The amount that will paid as interest per period reduces gradually as more and more portion of the paid balance is paid down while the portion of principal paid increases with further payments.

We the help of the table below, I will illustrate better

Period [email protected] Begin  Interest    Installment  Principal paid     Bal @ End

a                   b               c                  d                  e=d-c                 f=a-e

1             225,000      797           1,245                 448                224,552

2             224,599     795           1,245                  450               224,149

This method of loan repayment is called amortization on reducing balance.

Monthly interest

The monthly interest = Principal balance at the begin × interest rate per month

In period 1, interest = 225,000 × 4.25%/12= 797

Principal paid

Interest must be paid before principal, so principal paid in year 1

= Installment - Interest

= 1245- 797 = 448

Loan balance at the end

The balance of principal at the end of year 1

= Balance at the begin of year 1 - Principal paid in year 1

=225,000 -448= 224,552.

The same process is repeated for year 2. Doing we have a figure of

 224,149 as the  loan balance after the second repayment

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