Q:

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.

Accepted Solution

A:
Answer: 139,600.96Step-by-step explanation:We use the payment of a loan formula:[tex] \displaystyle PMT = \frac{P \left(\displaystyle \frac{r}{n}\right)}{\left[ 1 - \left( 1 + \displaystyle \frac{r}{n}\right)^{-nt} \right]} [/tex]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:  [tex] \displaystyle PMT = \frac{200000 \left(\displaystyle \frac{0.039}{12}\right)}{\left[ 1 - \left( 1 + \displaystyle \frac{0.039}{12}\right)^{-12(30)} \right]} [/tex]And using our calculator we get: PMT = $943.336Then the total amount of money paid in the mortgage is:  PMT*n*t = $943.336(12)(30) = $339,600.96Therefore, the interest paid is:  $339,600.96 - $200,000 = $139,600.96You have to enter it without $ and rounded to the nearest cent so: 139,600.96