Final answer:
The true yield on a $100,000 loan at a 6% interest rate with two discount points is higher than the nominal rate due to the prepaid interest from the points. The exact true yield requires a yield-to-maturity calculation, considering the upfront cost of the discount points. It is likely between 6.19% and 6.29% but requires precise calculations to confirm.
Step-by-step explanation:
The question at hand involves the calculation of a lender's true yield on a $100,000 loan with an interest rate of 6% for a 30-year term with annual payments, along with the cost of two discount points. A discount point is prepaid interest equal to 1% of the loan amount. Therefore, two discount points on a $100,000 loan would cost $2,000. This upfront cost-effectively increases the lender's yield above the nominal interest rate.
To calculate the true yield, we can use financial calculators or spreadsheet software to solve for the yield to maturity (YTM) on a bond that is analogous to the loan. Since the loan cost includes 2 discount points, the net amount the lender actually lends is $98,000 ($100,000 - $2,000), but the borrower will still pay back the loan based on the full $100,000. Using the inputs of PV = -$98,000 (present value, which is the amount the lender actually lends after the discount points), FV = $0 (future value, since the loan will be paid off at the end of the term), PMT = the annual payment based on a $100,000 loan at 6% interest, and N = 30 (number of years), we compute for the interest rate, which will give us the true yield to the lender.
Without access to the actual calculation tools or the specifics of the annual payment amount, we cannot provide the exact true yield here. However, we can be confident that the lender's true yield would be higher than the nominal rate of 6% due to the discount points, meaning options (c.) 6.19% and (d.) 6.29% would be more likely than (a.) 5.73% or (b.) 6.0%. The correct option from the offered choices could only be determined by the exact YTM calculation mentioned.