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You plan to purchase a $100,000 house using a 30-year mortgage obtained from your local credit...

Question:

You plan to purchase a {eq}\$100,000 {/eq} house using a {eq}30 {/eq}-year mortgage obtained from your local credit union. The mortgage rate offered to you is {eq}8.25 {/eq} percent. You will make a down payment of {eq}20 {/eq} percent of the purchase price.

A) Calculate your monthly payments on this mortgage.

B) Calculate the amount of interest and, separately, principal paid in the 25th payment.

Mortgage:

A mortgage is a loan used for the purpose of purchasing a house. The investor will be expected to make the payments from period to period to settle the loan amount plus the interest that will have accrued. The loan is the equivalent of the present value of the payments.

Answer and Explanation:

Price = $100,000

Down payment = 0.2 * 100,000 = 20,000

Loan = 100,000 - 20,000 = $80,000

n = 30 years adjusted for monthly payments = 30 *12 = 360

APR = 8.25% adjusted for monthly payments r =0.0825/12 = 0.006875

A) Calculate your monthly payments on this mortgage.

  • {eq}Loan = Payment * \dfrac{(1 - (1 + r )^{-n}) }{ r} {/eq}
  • {eq}80,000 = Payment * \dfrac{(1 - (1 + 0.006875 )^{-360}) }{0.006875} {/eq}
  • {eq}80,000 = Payment * 133.1085389 {/eq}
  • {eq}Payment=\dfrac{80,000 }{ 133.1085389} {/eq}
  • {eq}Payment= $601.01 {/eq}

B) Calculate the amount of interest and, separately, principal paid in the 25th payment.

Determine the loan balance after the 24th payment.

  • {eq}Loan \ balance = Payment * \dfrac{(1 - (1 + r )^{-(n-t)}) }{ r} {/eq}

n-t is the remaining loan term = 360 - 24 =336

  • {eq}Loan \ balance = 601.01 * \dfrac{(1 - (1 + 0.006875 )^{-336}) }{0.006875} {/eq}
  • {eq}Loan \ balance = 601.01 * 130.901969 {/eq}
  • {eq}Loan \ balance = $78,673.39 {/eq}

For the 25th payment

Interest paid;

  • Interest paid = 0.006875 * 78,673.39
  • Interest paid = $540.88

Principal Paid

  • Principal Paid = Monthly payment - interest paid
  • Principal Paid = 601.01 - 540.88
  • Principal Paid = $60.13

Learn more about this topic:

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Buying a House: Mortgage Types & Loan Length

from Finance 102: Personal Finance

Chapter 7 / Lesson 4
8.2K

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