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Brad decides to purchase a $240,000 house. He wants to finance the entire balance. He has received an APR of 2.7% for a 15-year mortgage. What is Brad’s total cost if he takes all 15 years to pay off the house? Round your answer to the nearest hundredth.

User Gospes
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Answer:

Brad's total cost for financing a $240,000 house at a 2.7% APR over 15 years is determined by calculating the monthly mortgage payment using the APR amortization formula and then multiplying it by the number of payments over the 15-year term.

Step-by-step explanation:

To calculate Brad's total cost of a $240,000 house with an APR of 2.7% for a 15-year mortgage, we use the formula for a fixed-rate mortgage payment:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]

Where:

M is the monthly payment.

P is the principal loan amount.

i is the monthly interest rate (annual rate divided by 12).

n is the number of payments (loan terms in years times 12).

Using the above information:

P = $240,000

i = 2.7% / 12 = 0.00225

n = 15 * 12 = 180

Next, we calculate the monthly payment and then the total cost of the house over 15 years:

M = $240,000 [ 0.00225(1 + 0.00225)^180 ] / [ (1 + 0.00225)^180 – 1 ]

M will equal a monthly payment which is multiplied by 180 to get the total cost of the loan after 15 years.

Without providing the exact mathematical operation and result here, Brad's total cost for the house over 15 years can be found by multiplying the monthly payment M by the number of payments n.

User Forivall
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