Surreal Corp. has borrowed to invest in a project. The loan calls for a payment of $17,500 every month for three years. The lender quoted Surreal a rate of 8.40 percent with monthly compounding. At what rate would you discount the payments to find the amount borrowed by Surreal Corp.? (Round to two decimal places.)

Question

Quizplus · Accepted Answer

To find the amount borrowed, we need to discount the stream of payments using the given interest rate. Let's use the formula for present value of an annuity:

PV = PMT x [1 - (1+r)^(-n)] / r

where PV is the present value of the annuity, PMT is the monthly payment, r is the monthly interest rate, and n is the total number of months.

Plugging in the given numbers, we get:

PV = 17500 x [1 - (1+0.07/12)^(-36)] / (0.07/12)
PV ≈ $548,880.62

So Surreal Corp. borrowed about $548,880.62 to invest in the project. Now let's calculate the effective annual rate (EAR) of the loan:

EAR = (1 + r/m)^m - 1

where m is the number of compounding periods per year. Plugging in the given numbers, we get:

EAR = (1 + 0.084/12)^12 - 1
EAR ≈ 8.73%

Therefore, choice B is the correct answer, and the other choices are either the given interest rate or incorrect calculations.