Cull Incorporated recently borrowed $250,000 from Century Bank when the prime rate was 4%. The loan was for 90 days with interest to be paid at the end of the period with a rate fixed at 1.5% above the prime rate. What is the total interest paid on this loan and what is the effective annual rate? (Assume a 365 day year.)
A) The total interest paid is $3390.41 and the effective annual rate is 5.62%.
B) The total interest paid is $13,750 and the effective annual rate is 5.62%.
C) The total interest paid is $13,750 and the effective annual rate is 5.55%.
D) The total interest paid is $3390.41 and the effective annual rate is 1.36%.

Question

Quizplus · Accepted Answer

The interest on the loan can be calculated using the following formula:

Interest = Principal x Rate x Time
where Principal = $250,000, Rate = Prime Rate + 1.5% = 4% + 1.5% = 5.5%, and Time = 90/365

Interest = $250,000 x 5.5% x (90/365) = $3390.41

The effective annual rate can be calculated using the following formula:

Effective Annual Rate = (1 + Interest Rate / m) ^ m - 1
where Interest Rate = 5.5%, m = 365/90

Effective Annual Rate = (1 + 5.5% / (365/90)) ^ (365/90) - 1 = 5.62%

Therefore, the total interest paid on the loan is $3390.41 and the effective annual rate is 5.62%. Choice A is correct.

Cull Incorporated Recently Borrowed $250,000 from Century Bank When the Prime