Discount Note Versus Ordinary Interest Loan
Northline Landscaping needs exactly $18,000 for eight months to buy a used trailer and mowers. Two financing offers are on the table. First, a bank offers a simple discount note with a face value of $18,000 and a 7.5% annual discount rate; the bank deducts the interest in advance, so Northline would receive less than $18,000 and would need to adjust the face value to net the full amount. Second, a credit union offers an ordinary simple interest loan at 7.9% annual interest for eight months, with interest paid at maturity and the full $18,000 available at the start. Northline can repay the loan early without penalty, but expects to hold it the full eight months. The owner wants to compare the true annual cost of each option, not just the quoted rates, and is uneasy about the discount note's upfront deduction.
1. For the discount note, compute the face value required to net $18,000, the discount, and the effective annual rate.
Read the worked answer
For a discount note, proceeds = face value x (1 - discount rate x time). Set proceeds equal to $18,000 and solve for face value:
Face = $18,000 / [1 - 0.075 x (8/12)] Face = $18,000 / (1 - 0.05) Face = $18,000 / 0.95 = $18,947.37
Discount = face - proceeds = $18,947.37 - $18,000 = $947.37. Check: $18,947.37 x 0.075 x (8/12) = $947.37.
Effective annual rate = (discount / actual proceeds) x (12/8) = ($947.37 / $18,000) x 1.5 = 0.0526315 x 1.5 = 0.078947, or about 7.89%.
The quoted 7.5% understates the true cost because the bank takes the interest out of the loan upfront, leaving Northline with less usable money.
2. For the credit union loan, compute the maturity interest, total repayment, and effective annual rate.
Read the worked answer
Ordinary simple interest = principal x rate x time = $18,000 x 0.079 x (8/12) = $18,000 x 0.079 x 0.6666667 = $948.00.
Total repayment at maturity = $18,000 + $948 = $18,948.
Effective annual rate = (interest / principal) x (12/8) = ($948 / $18,000) x 1.5 = 0.0526667 x 1.5 = 0.0790, or 7.90%.
Because the full $18,000 is available at the start and interest is paid at maturity, the quoted rate and the effective annual rate are essentially the same for an eight-month hold.
3. Compare the two offers and recommend one, considering cost, cash flow, and prepayment.
Read the worked answer
On a grossed-up basis, the discount note costs about $947.37, while the simple interest loan costs $948.00. The difference is only $0.63, so the quoted-rate advantage of the discount note is negligible.
The bigger issue is cash flow. The discount note requires a face value of $18,947.37 and gives Northline exactly $18,000 only if it is grossed up correctly. If Northline instead accepted a $18,000 face note, it would receive only $17,100 and be $900 short of its need.
Prepayment also favors ordinary interest: with an installment or simple interest loan, interest accrues on the outstanding balance, so early repayment saves interest. A discount note's interest is already deducted, making early repayment less valuable unless the note is structured otherwise.
Recommendation: take the credit union's 7.9% ordinary interest loan for simplicity, full principal availability, and easier prepayment. The discount note is marginally cheaper only if Northline is comfortable with the larger face amount and the upfront deduction.