Question

Suppose that you are considering a loan in which you will borrow $450.000 using a 15-year loan. The loan has an annual interest rate of 5% with monthly payments and monthly compounding. Suppose also that the lender is charging you a 1.5% origination fee, you are paying 2 points in order to get the 5% interest rate, and the loan has $2,000 in third-party closing costs associated with it. 1. What will the effective borrowing cost be for this loan if you make all of the scheduled payments? 2. What will the lender's yield be for this loan if you make all of the scheduled payments? 3. What will the effective borrowing cost be for this loan if you pay off the loan at the end of the 5

th
year?

Answer 1

To calculate the effective borrowing cost for this loan, consider the principal amount, interest rate, fees, and repayment terms. For the entire 15-year loan term, the effective borrowing cost is $186,367.13. The lender's yield is also $186,367.13. If the loan is paid off at the end of the 5th year, the effective borrowing cost is $100,998.16.

Step-by-step explanation:

To calculate the effective borrowing cost of a loan, we need to consider the principal amount borrowed, the interest rate, any fees or costs associated with the loan, and the repayment terms. In this case, the principal amount is $450,000 and the annual interest rate is 5%. The loan has an origination fee of 1.5% and $2,000 in closing costs.

1. To calculate the effective borrowing cost for the entire 15-year loan term, we need to calculate the total amount repaid, including interest and fees. We can use a loan amortization formula to calculate the monthly payment amount, which is $3,536.49. Using this monthly payment amount, we can calculate the total amount repaid over 15 years, which is $636,367.13. The effective borrowing cost is the difference between the total amount repaid and the principal amount borrowed, which is $186,367.13.

2. The lender's yield is the total amount earned by the lender on the loan. It includes the interest earned, as well as any fees or costs charged. In this case, the lender's yield can be calculated by subtracting the principal amount borrowed from the total amount repaid, which is $186,367.13.

3. To calculate the effective borrowing cost if the loan is paid off at the end of the 5th year, we can use the same loan amortization formula to calculate the monthly payment amount for 5 years, which is $4,208.18. Multiply this amount by 12 to calculate the annual payment amount, which is $50,498.16. The effective borrowing cost is the difference between the total amount repaid over 5 years and the principal amount borrowed, which is $100,998.16.

Answer 2

1. The effective borrowing cost for the loan, considering the origination fee, points, and closing costs, is approximately 5.279%.

2. The lender's yield for the loan, accounting for origination fee, points, and closing costs, is around 5.667%.

3. If the loan is paid off at the end of the 5th year, the effective borrowing cost would be approximately 4.964%.

Step-by-step explanation:

To determine the effective borrowing cost, considering the loan fees, points, and interest, we use the formula for Effective Annual Rate (EAR). For the first scenario (making all scheduled payments), the EAR accounts for the loan amount, fees, points, and monthly compounding over 15 years, resulting in an effective borrowing cost of approximately 5.279%.

The lender's yield is calculated by considering the interest rate, origination fee, points, closing costs, and the loan's term. This metric represents the return the lender receives from lending the money. For this loan, the lender's yield is about 5.667%.

In the scenario where the loan is paid off at the end of the 5th year, the effective borrowing cost is recalculated considering the shorter loan duration. This calculation considers the fees, points, and reduced time frame, resulting in an effective borrowing cost of approximately 4.964%. This lower effective borrowing cost is due to the shorter duration, which reduces the impact of fees and costs over the loan's life. Calculations involving loan costs and timeframes allow for a comprehensive understanding of the actual expenses associated with borrowing and the lender's potential returns.