The Jordan family recently purchased their first home. The house has a 15-year (180-month),...

Question:

The Jordan family recently purchased their first home. The house has a 15-year (180-month), $165,000 mortgage. The mortgage has a nominal annual interest rate of 7.75%. All mortgage payments are made at the end of the month. What will be the remaining balance on the mortgage after one year (right after the 12th payment has been made)?

Mortgage Payments:

Mortgage payments are used to pay off the loan with equal installments. The principal is reduced with each payment and the outstanding loan gets smaller and smaller. The payment shall depend on the amount of outstanding loan, the interest rate and the time period of the loan.

Answer and Explanation:

The loan payment can be calculates as:

{eq}Payment = \dfrac {Loan\:Value}{\dfrac{1-(1+r)^{-n}}{r}} {/eq}

Here:

  • Payment = ?
  • Loan Value = $165,000
  • r (rate) = 7.75%/12 = 0.006458333
  • n = 180

Substituting the values we have:

{eq}Payment = \dfrac { $ 165,000}{\dfrac{1-(1+0.006458333)^{-180}}{0.006458333}} {/eq}

{eq}Payment = \dfrac { $ 165,000} {106.2387931} {/eq}

{eq}Payment = $1,553.10 {/eq}


The formula for outstanding loan balance can be written as:

{eq}FV= (Amount\:Borrowed \times ((1+r)^{n}) - Payment \times \dfrac{(1+r)^{n}-1}{r} {/eq}

  • FV is the outstanding amount after n periods.
  • Payment = $1,553.10
  • Amount borrowed = $165,000
  • r (rate) = 7.75%/12 = 0.006458333
  • n = 12

{eq}FV= ($165,000 \times ((1+0.006458333)^{12}) - $1,553.10 \times \dfrac{(1+0.006458333)^{12}-1}{0.006458333} {/eq}

{eq}FV= $178,251.64 - $19,313.73 {/eq}

{eq}FV= $158,937.91 {/eq}

Hence the remaining mortgage balance after 12th payment is $158,937.91.


Learn more about this topic:

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Calculating Monthly Loan Payments

from Remedial Algebra I

Chapter 25 / Lesson 8
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