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You have found your dream home and would like to purchase it by using a mortgage loan. However,...

Question:

You have found your dream home and would like to purchase it by using a mortgage loan. However, suppose that you can only afford to pay a maximum of $1500 per month. If a bank charges you an interest rate of 4.7%, compounded quarterly, how much money can you borrow? Assume a 30-year mortgage.

Mortgage:

Mortgage is a loan borrowed to finance the purchase of a house. The terms of the mortgage include the amount, term period of the loan, and the interest rate to be charged. The mortgage amount is the equivalent of the present value of the periodic mortgage payments made by the borrower.

Answer and Explanation:

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

Monthly payment = $1,500

APR = 4.7%

n = 30 years

How much money can you borrow?

Note that the interest is compounded quarterly but the payments are made on a monthly basis. Determine the equivalent annual rate.

  • {eq}i = q * [(1 + \dfrac{r}{m} )^{m/q)}-1 ] {/eq}

i is the equivalent annual rate

q is the number of payments in a year

r is the nominal annual rate

m is the number of compounding periods in a year

  • {eq}i = 12 * [(1 + \dfrac{0.047}{4} )^{4/12)}-1 ] {/eq}
  • {eq}i = 12 * [(1 + \dfrac{0.047}{4} )^{4/12)}-1 ] {/eq}
  • {eq}i = 0.0468 {/eq}
  • {eq}i = 4.68% {/eq}

Calculate the loan amount;

Adjusting for monthly payment

n = 30*12 = 360

r = 0.0.0468/12 =0.0039

  • {eq}Loan = 1,500 * \dfrac{(1 - (1 +0.0039 )^{-360}) }{0.0039} {/eq}
  • {eq}Loan = 1,500 * 193.2604724 {/eq}
  • {eq}Loan = $289,890.71 {/eq}

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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