Carborundum Metals issues commercial paper with a face value of $1,000,000 and a maturity of three months. Carborundum receives net proceeds of $992,000 when it sells the paper. If the prime rate is 8% APR compounded quarterly, how much savings in interest did Carborundum realize by accessing the commercial paper market?
To calculate the savings in interest realized by Carborundum, we first need to determine the interest expense for three months if Carborundum were to borrow the funds at the prime rate.
Step 1: Calculate the annual interest rate.
Since the prime rate is given as 8% APR, we need to convert it to a quarterly interest rate.
Quarterly Interest Rate = APR / Number of Compounding Periods per Year
Quarterly Interest Rate = 8% / 4 = 2%
Step 2: Calculate the interest for three months.
Interest = Principal x Rate x Time
Principal = $1,000,000
Rate = Quarterly Interest Rate = 2%
Time = 3 months / 12 months = 0.25 (since we need the time in years)
Interest = $1,000,000 x 2% x 0.25 = $5,000
Step 3: Calculate the net proceeds after deducting the interest expense.
Net Proceeds = Face Value - Interest Expense
Net Proceeds = $1,000,000 - $5,000 = $995,000
Step 4: Calculate the savings in interest.
Savings in Interest = Net Proceeds from Commercial Paper - Net Proceeds from borrowing at the prime rate
Savings in Interest = $992,000 - $995,000 = -$3,000
Based on the calculations, Carborundum did not realize savings in interest by accessing the commercial paper market, but actually incurred an additional expense of $3,000 compared to borrowing at the prime rate.