The price of a home is $219 comma 000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed-rate mortgage at 10%. Find the total cost of interest over 30 years.
Question
The price of a home is $219 comma 000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed-rate mortgage at 10%. Find the total cost of interest over 30 years.
Solution
Sure, here's how to calculate the total cost of interest over 30 years:
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Calculate the down payment: 20% of 43,800.
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Subtract the down payment from the total price to find the loan amount: 43,800 = $175,200.
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Calculate the points: 3 points of 5,256.
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Add the points to the loan amount: 5,256 = $180,456. This is the total amount that will be financed.
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Calculate the monthly payment using the formula for a fixed-rate mortgage: M = P[r(1+r)^n]/[(1+r)^n – 1], where P is the loan amount, r is the monthly interest rate, and n is the number of payments. The annual interest rate is 10%, so the monthly rate is 10%/12 = 0.00833. The number of payments is 30 years * 12 months/year = 360. Plugging these values into the formula gives: M = 1,590.75.
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Multiply the monthly payment by the number of payments to find the total amount paid over the life of the loan: 572,670.
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Subtract the original loan amount to find the total cost of interest: 180,456 = $392,214.
So, the total cost of interest over 30 years is $392,214.
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