Question

You plan to purchase a $200,000 house using a 15-year mortgage obtained from your local credit union. The mortgage rate offered to you is 4.5 percent. You will make a down payment of 20 percent of the purchase price. a.Calculate your monthly payments on this mortgage. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) Monthly payment $

b.Calculate the amount of interest and, separately, principal paid in the 20th payment. (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))
Amount of interest $
Amount of principal$ c.Calculate the amount of interest and, separately, principal paid in the 100th payment. (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))
Amount of interest $
Amount of principal$ d.Calculate the amount of interest paid over the life of this mortgage. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))
Amount of interest paid$

Answer 1

The student's question on calculating mortgage payments, principal, interest for specific payments, and total interest over the life of a 15-year mortgage can be addressed using the annuity payment formula and an amortization schedule.

Step-by-step explanation:

To calculate the monthly payments on a $200,000 house with a 15-year mortgage at a 4.5% interest rate after a 20% down payment, we first determine the loan amount: $200,000 - (20% of $200,000) = $200,000 - $40,000 = $160,000. The monthly interest rate is 0.045/12, and the number of payments is 15*12. Using the formula for the monthly payment (PMT) of an annuity:

PMT = [P*r(1+r)^n] / [(1+r)^n - 1], where P is the principal, r is the monthly interest rate, and n is the total number of payments.

Calculating the amount of interest and principal paid in the 20th and 100th payment, and the total interest paid over the life of the mortgage would require applying the calculated monthly payments to an amortization schedule to break down the principal and interest components of each payment.