A merchant receives an invoice for a motor boat for $20,000 with credit terms 4/30, n/100 (4% discount if paid within 30 days; otherwise full amount due in 100 days). What is the highest simple annual interest rate (in %) at which he can borrow money to take advantage of the discount?

Introduction / Context:
This question is about comparing a cash discount against the cost of borrowing money. Under terms 4/30, n/100, the buyer can either pay early at day 30 with a 4% discount, or pay the full amount at day 100. Taking the discount means paying earlier, which may require borrowing. The “highest interest rate he can afford” is the break-even rate where interest cost of borrowing equals the discount savings. This is a standard trade credit annualization problem.

Given Data / Assumptions:

• Invoice amount = $20,000
• Discount = 4% if paid in 30 days
• Otherwise pay full in 100 days
• Extra time gained by not taking discount = 100 - 30 = 70 days
• Borrow amount needed to take discount = discounted price
• Use simple interest with a 360-day financial year (common convention for such problems)

Concept / Approach:
Discounted payment at day 30:
Discounted price = 20000 * (1 - 0.04) = 19200 Savings from discount: Savings = 20000 - 19200 = 800 If borrowing $19,200 for 70 days, the break-even annual rate R satisfies: Interest = Principal * R * (70/360) = Savings

Step-by-Step Solution:
Discounted price = 19200 Savings = 800 Let annual simple rate = R (in decimal) Borrowing time = 70/360 years Break-even: 19200 * R * (70/360) = 800 R = 800 * 360 / (19200 * 70) R = (800/19200) * (360/70) 800/19200 = 0.0416667 360/70 ≈ 5.142857 R ≈ 0.2142857 Rate (%) ≈ 21.43%

Verification / Alternative check:
If the borrowing rate is lower than 21.43%, the interest cost for 70 days is less than $800 savings, so taking the discount is beneficial. If the rate is higher, borrowing costs exceed savings, so skipping the discount is better.

Why Other Options Are Wrong:
18%, 15% are below the break-even, meaning discount is still beneficial (not the highest). 24% and 30% are above break-even and would make borrowing too costly compared to the discount savings.

Common Pitfalls:
Using the full invoice amount $20,000 as the borrowed amount instead of $19,200, using 100 days instead of the 70-day difference, or forgetting to annualize by dividing by (70/360).

Final Answer:
The highest simple annual interest rate is approximately 21.43%.