Question

You plan to purchase a $160,000 house using a 15 -year mortgage obtained from your local credit union. The mortgage rate offered to you is 7.85 percent. You will make a down payment of 20 percent of the purchase price. a. Calculate your monthly payments on this mortgage. b. Calculate the amount of interest and, separately, principal paid in the 20th payment. c. Calculate the amount of interest and, separately, principal paid in the 100 th payment. d. Calculate the amount of interest paid over the life of this mortgage. (For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

Answer 1

The monthly payments on a $160,000 house with a 15-year mortgage and 7.85% interest rate, the monthly payment is approximately $1,265.56.

Step-by-step explanation:

To calculate the monthly payments on this mortgage, we first need to calculate the loan amount. The purchase price of the house is $160,000 and the down payment is 20% of that, which is $32,000. So the loan amount is $160,000 - $32,000 = $128,000.

To calculate the monthly payments, we can use the formula for calculating the monthly payment on a fixed-rate mortgage:

Monthly Payment = Loan Amount * (Interest Rate / 12) / (1 - (1 + Interest Rate / 12)^(-Number of Payments))

Plugging in the values, we get:

Monthly Payment = $128,000 * (0.0785 / 12) / (1 - (1 + 0.0785 / 12)^(-15 * 12))

After evaluating this expression, we find that the monthly payment on this mortgage is approximately $1,265.56.

Answer 2

To answer the student's questions on mortgage payments and interest, calculate the monthly payment using the loan formula, then analyze an amortization schedule for interest and principal breakdown at specified payments. The total interest paid is the sum of all interest payments over the life of the mortgage.

Step-by-step explanation:

To calculate the monthly payments and interest over the life of the mortgage, the student should use the following formula for an amortizing loan's regular payment amount:

PMT = P * r(1+r)^n / ((1+r)^n - 1)

Where:
PMT is the monthly payment
P is the principal amount (after down payment)
r is the monthly interest rate (annual rate divided by 12)
n is the total number of payments (months for the life of the loan)

For part a), the student will calculate the monthly payment using the mortgage amount after the 20% down payment, with a 7.85% annual interest rate, over 15 years (180 payments).

For parts b) and c), the student will need to analyze the amortization schedule to determine specific amounts of interest and principal paid at different stages of the mortgage.

Finally, for part d), the student will sum all interest payments over the life of the mortgage, which can be calculated directly from the mortgage payment and the number of payments, or derived from the amortization schedule.