Simple Interest on Debentures Paid Quarterly: Jaclyn buys $50,000 worth of debentures that earn 9.5% per annum simple interest, paid quarterly (every 3 months). If the debenture term is 18 months, what is the total simple interest earned over the full term (in $)?

Introduction / Context:
This problem asks you to compute simple interest on debentures where interest is paid quarterly. Although payments are quarterly, the underlying rate is annual and the interest is still simple, not compound. The key is to convert the total term into years and then apply the simple interest formula to find the total interest over the entire period.

Given Data / Assumptions:

• Principal P = $50,000.
• Annual simple interest rate r = 9.5% per annum.
• Interest is paid quarterly, but interest is simple (no compounding).
• Term of the debentures = 18 months.

Concept / Approach:
Under simple interest, the timing of payments (monthly, quarterly, or annually) does not affect the total interest; what matters is the total time in years, principal, and rate. We convert 18 months into years, then use I = (P * r * t) / 100. The quarterly payments simply mean this total interest will be split into 6 equal payments, but the total accumulated interest is what the question asks for.

Step-by-Step Solution:
Step 1: Convert the term into years: 18 months = 18 / 12 = 1.5 years. Step 2: Use the simple interest formula I = (P * r * t) / 100. Step 3: Substitute P = 50,000, r = 9.5, and t = 1.5. Step 4: I = (50,000 * 9.5 * 1.5) / 100. Step 5: First compute 9.5 * 1.5 = 14.25. Step 6: Then I = (50,000 * 14.25) / 100 = 50,000 * 0.1425. Step 7: Multiply: 50,000 * 0.1425 = $7,125. Step 8: Therefore, the total simple interest over 18 months is $7,125.

Verification / Alternative check:
You can think of it quarterly: 18 months is 6 quarters. Annual interest is (50,000 * 9.5) / 100 = $4,750. For 1.5 years, that is 4,750 * 1.5 = 7,125. This consistent approach confirms the previous result.

Why Other Options Are Wrong:

• $8,125 and $9,125: Both are larger than the correct amount and would correspond to higher rates or compound interest, which are not given.
• $6,125: Too small and does not match 9.5% over 1.5 years.
• $7,500: Slightly larger than the correct interest and does not fit the exact calculation.

Common Pitfalls:
Some candidates mistakenly compound the interest quarterly or try to use a quarterly rate of 9.5 / 4% with compounding, which is not required here. Others forget to convert months to years before using the simple interest formula. Always read whether interest is simple or compound and handle time units carefully.

Final Answer:
The total simple interest earned over 18 months is $7,125.