Question

Calculate the total interest paid on a 30-year, 3.9% fixed-rate $200,000 mortgage loan.

Remember that number of compounding periods in a year n = number of payments expected to be made in a year. If you make monthly mortgage payments, then interest on the loan is compounded monthly.

Give answer in dollars rounded to the nearest cent. Do NOT enter "$" sign in answer.

Answer 1

139,600.96

Explanation:

We use the payment of a loan formula:

`\displaystyle PMT = (P \left(\displaystyle (r)/(n)\right))/(\left[ 1 - \left( 1 + \displaystyle (r)/(n)\right)^(-nt) \right])`

P is the principal: $200,000. t is the number of years: 30, n is 12 since it is compounded monthly. And r is 0.039 which is 3.9% in decimal form (3.9/100)

So the formula becomes:

`\displaystyle PMT = (200000 \left(\displaystyle (0.039)/(12)\right))/(\left[ 1 - \left( 1 + \displaystyle (0.039)/(12)\right)^(-12(30)) \right])`

And using our calculator we get: PMT = $943.336

Then the total amount of money paid in the mortgage is:

PMT*n*t = $943.336(12)(30) = $339,600.96

Therefore, the interest paid is:

$339,600.96 - $200,000 = $139,600.96

You have to enter it without $ and rounded to the nearest cent so: 139,600.96