"a borrower 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? "

Principal balance after the second payment is applied is $243,233.49

Explanation:

Initial principal                              $ 225,000

Interest due (4.25% x 225,000)   $ 9562.50

1st payment                                    -$1,245

Principal balance after 1st pay    $233,317.5

Interest due (4.25% x 233,317.5)    $9,915.99

2nd payment                                  -$1,245

Principal balance after 2nd pay    $243,233.49

The answer is: $ 241, 988.4938

Explanation:

A mortgage is a debt security wherein the recipient guarantees repayment of the debt by providing collateral in form of property. The debtor repays the debt at a fixed interest rate in fixed instalments at a specified amount for the life of the debt. The longer the period of repayment, the lower the instalments and the higher the interest. The borrower has acquired a fixed-rate mortgage where the interest payment and instalments paid do not change over the life of the debt. Should market interest rates drop significantly, then the borrower may opt to refinance the loan so as to secure a lower interest rate.

To calculate the balance of the principal after the second payment, the specific terms of the debt instrument must be outlined:

Duration (N) = 30 years

Present value of debt (PV) = $225, 000

Instalments/payments (PMT) = - ($1245)

Interest rate (i) = 4.25%

Interest Value (I) = interest accrued for the period

Year 1 (I)  = $1, 245

Year 2 (I) = $1, 245

C = accrued amount to be capitalised to the principal balance

Year 1 (C) = 4.25%(0.0425 * $225, 000) - $1, 245

Year 2 (C) = 4.25%(0.0425 * $233, 317.5) - $1, 245

The Accrued interest during the year less the interest payment made equals the amount of interest that is capitalised to the principal amount and forms the basis of the following year's interest computation.

An amortisation table provides a tabular format of analysing the debt:

                PMT                 I                         C                    Principal balance    

Year 0        _                       _                         _                     $225, 000

Year 1    ($1245)           $9, 562.5            $8317.5              $233, 317.5

Year 2    ($1245)         $9, 915.99375     $8, 670.99375  $241,988.4938      

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