Question

Largent Supplies Corp. has borrowed to invest in a project. The loan calls for a payment of $17,384 every month for three years. The lender quoted Largent a rate of 8.40 percent with monthly compounding. At what rate would you discount the payments to find the amount borrowed by Largent?

a. 8%
b. 8.5%
c. 9%
d. 9.5%

Answer 1

The amount borrowed by Largent Supplies Corp. should be discounted at the monthly equivalent of the annual rate quoted by the lender, which is 0.7% per month or 8.4% annually, compounded monthly. The closest option is 8.5% per annum.

Step-by-step explanation:

To find the amount borrowed by Largent Supplies Corp., we must discount the future monthly payments using the rate quoted by the lender. Since the lender quoted an 8.40 percent rate with monthly compounding, the monthly discount rate would be the annual rate divided by 12 (the number of months in a year). Therefore, to find the present value of the loan payments, you should discount the payments at the monthly equivalent of the annual rate, which is 0.7% per month (8.4 percent annual rate divided by 12). The correct answer is not directly provided as an option, but you can infer it by converting the annual rate to a monthly rate.

The closest available option that represents this monthly discount rate is b. 8.5% per annum, as none of the options translates exactly to 0.7% monthly. However, the exact rate used for discounting to find the loan amount would be 0.7% per month, translating to 8.4% annually with monthly compounding.