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You want to buy a house that costs $230,000. You will make a down payment equal to 10 percent of the price of the house and finance the remainder with a loan that has an APR of 5.27 percent compounded monthly. If the loan is for 20 years, what are your monthly mortgage payments?

User Biswa
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1 Answer

4 votes

Answer:

$1,397.17

Explanation:

To calculate the monthly mortgage payments, we need to determine the loan amount after the down payment and then use Monthly Payment Formula to calculate the monthly payments.

Monthly Payment Formula


\boxed{PMT=(PVi\left(1+i\right)^n)/(\left(1+i\right)^n-1)}

where:

  • PMT = Monthly payment.
  • PV = Loan amount.
  • i = Interest rate per month (in decimal form).
  • n = Term of the loan (in months).

If the house costs $230,000, and a down payment equal to 10% of the price of the house is made, then the value of the loan (PV) is:


PV=230000 \cdot 90\%=\$207,000

If the APR is 5.27%, then the value of i is:


i = (0.0527)/(12)

If the term of the loan is 20 years, then the value of n is:


n = 20 \cdot 12 = 240 \; \sf months

Substitute the values into the formula:


PMT=(207000 \cdot (0.0527)/(12)\left(1+(0.0527)/(12)\right)^(240))/(\left(1+(0.0527)/(12)\right)^(240)-1)

Using a calculator to evaluate, we get:


PMT=1397.17122...


PMT=1397.17

Therefore, the monthly mortgage payment would be approximately $1,397.17 (to the nearest cent).

You want to buy a house that costs $230,000. You will make a down payment equal to-example-1
User Thykof
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