Question

Assume a $175,000 mortgage loan and 10-year term. The lender is charging an annual interest rate of 6 percent and 4 discount points at origination.

a. What is the monthly payment assuming that it is based on an amortization period of 30 years?
b. What will be the required balloon payment at the end of the tenth year?
c. What is the effective borrowing cost on the loan if it is held to maturity?

Answer 1

The monthly payment on a $175,000 mortgage at 6% interest over 30 years can be calculated using loan formulas, but the exact amount will need adjustments for discount points. The balloon payment after ten years and effective borrowing cost to maturity depend on additional calculations considering the loan's specific terms and time value of money.

Step-by-step explanation:

Calculating Mortgage Payments and Effective Borrowing Cost

To answer the student's question regarding the monthly payment on a $175,000 mortgage loan with a 10-year term, annual interest rate of 6%, and 4 discount points at origination, assuming an amortization period of 30 years:

a. To find the monthly payment, you first need to calculate the applicable monthly interest rate by dividing the annual rate by 12 (months). This would be 0.06 / 12 = 0.005 (0.5%). Then, we would use the formula for an amortizing loan to find the monthly payment. However, since an exact formula would be complex due to the inclusion of discount points, it's typically easier to use an online mortgage calculator or formulas provided in financial calculators.

b. The balloon payment at the end of the tenth year would require calculating the remaining balance of the loan after 120 monthly payments have been made. This is done by finding the future value of the remaining loan balance, which is essentially a present value calculation using the remaining amortization period of 20 years.

c. Calculating the effective borrowing cost if the loan is held to maturity involves considering all the payments made over the full term, including the discounted points paid upfront, any closing costs, and monthly payments. The effective interest rate would account for the time value of money and provide a more accurate reflection of the cost of borrowing.

Answer 2

a. The monthly payment assuming a 30-year amortization period would be $1,049.02. b. The required balloon payment at the end of the 10th year would be $138,903.98. c. The effective borrowing cost on the loan, if held to maturity, would be $190,903.98.

Step-by-step explanation:

To calculate the monthly payment for a mortgage loan, we can use the formula:

PMT = P × (r(1+r)^n) / ((1+r)^n-1)

Where PMT is the monthly payment, P is the loan amount, r is the monthly interest rate, and n is the number of monthly payments.

a. Using the formula above, with P = $175,000, r = 6% / 12 = 0.005, and n = 30 × 12 = 360, we can calculate the monthly payment to be $1,049.02.

b. A balloon payment is a larger lump sum payment that is due at the end of the loan term. In this case, since the loan term is 10 years, the balloon payment would be the remaining balance of the loan at the end of the 10th year. To calculate the balloon payment, we can use the formula:

Balloon payment = P × (1 + r)^n

Using the formula above, with P = $175,000, r = 6% / 12 = 0.005, and n = 10 × 12 = 120, we can calculate the balloon payment to be $138,903.98.

c. The effective borrowing cost takes into account both the interest rate and any upfront fees, such as the discount points. In this case, the lender is charging 4 discount points at origination. Each discount point is equal to 1% of the loan amount. So, in this case, 4 discount points would be equal to 4% of $175,000, which is $7,000. To calculate the effective borrowing cost, we can add the upfront fees to the total interest paid over the life of the loan. Thus, the effective borrowing cost would be the total interest paid plus the upfront fees, which is $183,903.98 + $7,000 = $190,903.98.