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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.

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Solution

Sure, here's how to calculate the total cost of interest over 30 years:

  1. Calculate the down payment: 20% of 219,000is219,000 is 43,800.

  2. Subtract the down payment from the total price to find the loan amount: 219,000219,000 - 43,800 = $175,200.

  3. Calculate the points: 3 points of 175,200is175,200 is 5,256.

  4. Add the points to the loan amount: 175,200+175,200 + 5,256 = $180,456. This is the total amount that will be financed.

  5. 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 = 180,456[0.00833(1+0.00833)360]/[(1+0.00833)3601]=180,456[0.00833(1+0.00833)^360]/[(1+0.00833)^360 – 1] = 1,590.75.

  6. Multiply the monthly payment by the number of payments to find the total amount paid over the life of the loan: 1,590.75360=1,590.75 * 360 = 572,670.

  7. Subtract the original loan amount to find the total cost of interest: 572,670572,670 - 180,456 = $392,214.

So, the total cost of interest over 30 years is $392,214.

This problem has been solved

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