Jaclyn buys company debentures worth $50,000 and earns 9.5% simple interest per annum, paid every quarter (every 3 months). If the agreed term of the debentures is 18 months, what amount of simple interest will she receive at the end of each quarter?

Introduction / Context:
This question tests the basic application of the simple interest formula when interest is quoted per annum but actually paid at regular sub annual intervals, in this case quarterly. Many savings products and debentures pay investors their interest every month, quarter, or half year rather than only once at maturity. The key skill is to compute the total simple interest over the full term in years and then divide it correctly across the number of payment periods to find the interest amount per period.

Given Data / Assumptions:

Principal invested in debentures = $50,000
Annual simple interest rate = 9.5 percent per annum
Total investment term = 18 months
Interest is paid every quarter, that is once every 3 months
Assume simple interest with no reinvestment of interest payments

Concept / Approach:
Under simple interest, the interest depends only on the original principal, the annual rate, and the total time in years. The standard formula is:
Simple interest I = P * R * T Here P is the principal, R is the rate per year written as a decimal, and T is the time in years. Once the total simple interest over the full 18 months is known, it can be shared equally between the number of quarters in 18 months, because each quarter earns the same simple interest amount.

Step-by-Step Solution:
Step 1: Convert the total time of 18 months to years. T = 18 months / 12 = 1.5 years. Step 2: Convert the annual rate of 9.5 percent to decimal. R = 9.5 percent = 9.5 / 100 = 0.095. Step 3: Apply the simple interest formula for the entire 1.5 years. I = P * R * T = 50,000 * 0.095 * 1.5. I = 50,000 * 0.1425 = 7,125 dollars. Step 4: Find the number of quarters in 18 months. 18 months / 3 months per quarter = 6 quarters. Step 5: Interest per quarter = total interest / number of quarters. Interest each quarter = 7,125 / 6 = 1,187.50 dollars.

Verification / Alternative check:
Another way is to think directly in quarterly terms. Each year has 4 quarters. Since the annual simple interest is 50,000 * 0.095 = 4,750 dollars per year, the simple interest for one quarter is 4,750 / 4 = 1,187.50 dollars. There are 6 quarters in 18 months, so 1,187.50 * 6 = 7,125 dollars total, which matches the earlier calculation. This confirms the quarterly interest figure is correct.

Why Other Options Are Wrong:
Option $1,234.00 is larger than the correct quarterly interest and does not correspond to dividing the total simple interest evenly over six quarters. Option $1,289.00 gives an even higher quarterly amount and would imply a much greater annual interest than 9.5 percent. Option $1,345.00 is even more unrealistic and would imply more than the total simple interest that should be earned over the 18 month period when multiplied by six.

Common Pitfalls:
A frequent error is to treat 18 months as 18 years or as 2 years, which leads to large mistakes in the time factor. Another common mistake is to forget that the given 9.5 percent applies per annum and does not change simply because interest is paid quarterly. Some learners also divide the annual interest by 3 instead of 4 when trying to find the quarterly interest. Always convert time to years, compute the total simple interest correctly, and then divide by the exact number of periods for which payments are made.

Final Answer:
The fixed simple interest amount that Jaclyn receives at the end of each quarter is $1,187.50.