Wentworth Greenery harvests its crops four times annually and receives payment for its crop 90 days after it is picked and shipped.However, the firm must plant, irrigate, and harvest on a near continual schedule.The firm uses 90-day bank notes to finance its operations.The firm arranges an 11 percent discount interest loan with a 20 percent compensating balance four times annually.What is the effective annual rate of these discount loans?
A)11.00%
B)15.94%
C)11.46%
D)13.75%
E)12.72%

Question

Quizplus · Accepted Answer

First, we need to calculate the effective interest rate for each discount loan:

Effective Interest Rate = [1 - (Discount %)] x [365/(Loan Period - Discount Period)]

Loan Period = 90 days
Discount Period = 11 days (11% of 90 days)
Discount % = 11%

Effective Interest Rate = [1 - (0.11)] x [365/(90 - 11)]
Effective Interest Rate = 0.891 x 4.402
Effective Interest Rate = 3.92 or 3.92%

Next, we need to calculate the effective annual rate (EAR) of the four discount loans using the following formula:

EAR = [(1 + r/n)^n - 1]

r = effective interest rate
n = number of times the loan is issued per year (in this case, 4 times)

EAR = [(1 + 0.0392/4)^4 - 1]
EAR = 0.1594 or 15.94%

Therefore, the effective annual rate of these discount loans is 15.94%, and the best choice is B.

Wentworth Greenery Harvests Its Crops Four Times Annually and Receives