Jaclyn buys $50,000 worth of debentures. She earns 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 is simple interest over a term expressed in months, with interest paid quarterly. Under simple interest, the total interest over the whole term does not depend on how frequently it is paid; quarterly payments just split the same total interest into 3-month chunks. So we can compute total interest using I = P * r * t, where t is in years, and r is annual rate in decimal form. Then, if needed, we can interpret how it would be distributed across quarters, but the question asks the total interest over 18 months.

Given Data / Assumptions:

• Principal, P = $50,000
• Annual simple interest rate = 9.5% per annum
• Time = 18 months = 18/12 = 1.5 years
• Simple interest formula: I = P * r * t
• Quarterly payment detail does not change the total interest

Concept / Approach:
Convert rate to decimal and time to years:
r = 9.5% = 0.095 t = 1.5 years Then calculate interest directly using I = P * r * t.

Step-by-Step Solution:
I = 50000 * 0.095 * 1.5 First, 0.095 * 1.5 = 0.1425 I = 50000 * 0.1425 = 7125 Total simple interest earned = $7,125

Verification / Alternative check:
Quarterly interest payment would be for 3 months = 0.25 year. Each quarter interest = 50000*0.095*0.25 = 1187.5. Over 6 quarters (18 months), total = 1187.5*6 = 7125, confirming the result.

Why Other Options Are Wrong:
$8,125 and $9,125 would correspond to higher rate or longer term. $6,125 corresponds to a lower effective rate. $7,500 is too high for 9.5% over 1.5 years on $50,000.

Common Pitfalls:
Using 18 months as 18 years, forgetting to convert 9.5% to 0.095, or assuming quarterly payments mean compounding (the question states simple interest).

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