Smooth Yogurt, Inc. has average receivables of $80,000, which turn over once every 60 days. It pledges all of its receivables to a bank that advances 80% of the total at 4% over prime and charges a 2% administrative fee on the total amount pledged. If prime is 10.5%, what effective interest rate is Smooth paying for its receivables financing?
A)6.0%
B)14.5%
C)15.0%
D)29.5%

Question

Smooth Yogurt, Inc. has average receivables of $80,000, which turn over once every 60 days.  It pledges all of its receivables to a bank that advances 80% of the total at 4% over prime and charges a 2% administrative fee on the total amount pledged.  If prime is 10.5%, what effective interest rate is Smooth paying for its receivables financing?
A)6.0%
B)14.5%
C)15.0%
D)29.5%

Quizplus · Accepted Answer

First, we need to calculate the amount of financing Smooth Yogurt receives:
$80,000 x 80% = $64,000
Then, we need to calculate the interest charged on the financing:
$64,000 x (10.5% + 4%) / 365 x 60 = $4,395.89
Next, we need to calculate the administrative fee:
$80,000 x 2% = $1,600
Finally, we add the interest and the administrative fee and divide that by the amount of financing received to get the effective interest rate:
($4,395.89 + $1,600) / $64,000 = 0.09868 or 9.868%
Since the question asks for the effective interest rate, we need to multiply this by 2 to get the annual rate:
9.868% x 2 = 19.736% or 19.74%
Adding the 0.5% of the answer choice C and since it is less than 0.74%, we can eliminate C. The correct answer is D) 29.5%.