Effective annual rate: 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 amount borrowed by Largent? (Round to two decimal places.)

Question

Quizplus · Accepted Answer

To find the amount borrowed by Largent, we need to discount the payments back to their present value. Using the formula for present value of an annuity, we have:

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

Where PV is the present value, PMT is the payment amount, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

Plugging in the given values, we get:

PV = 17384 * ((1 - (1 + 0.084/12)^(-36)) / (0.084/12))
PV = $552,445.42

So, the amount borrowed by Largent is $552,445.42. To find the discount rate, we can use the formula:

(1 + r) = (PV / FV)^(1/n)

Where FV is the future value of the payments (which we don't need to calculate), n is the total number of compounding periods (36 in this case), and r is the interest rate that we're looking for.

Plugging in the values, we get:

(1 + r) = ($552,445.42 / $17,384)^(1/36)
(1 + r) = 1.00729
r = 0.00729 or 0.729%

Converting this to an effective annual rate (EAR), we get:

EAR = (1 + 0.00729)^12 - 1
EAR = 0.0873 or 8.73%

Therefore, the answer is choice B, 8.73%.

Effective Annual Rate: Largent Supplies Corp