Determine the ordinary simple interest, using a 360 day year convention, on a 90 day loan of $8,000 at a simple interest rate of 8.5% per annum.

Introduction / Context:
Banks and finance companies sometimes use the ordinary simple interest method, where a 360 day year is assumed for convenience instead of the actual 365 day year. This question checks whether you can correctly convert days to a fraction of a year, apply the simple interest formula, and interpret the meaning of an annual percentage rate when the borrowing period is less than one full year.

Given Data / Assumptions:

Loan principal P = $8,000
Annual simple interest rate R = 8.5 percent per annum
Loan term = 90 days
A 360 day year is used for time conversion (ordinary simple interest)
No part repayments are made during the 90 day term

Concept / Approach:
For ordinary simple interest, time in years is calculated by dividing the number of days by 360. Then the simple interest formula I = P * R * T is applied. Here, R must be expressed as a decimal, and T is the time in years. Since the borrowing period is less than one year, the interest earned will be a fraction of the annual interest that the principal would generate in a full year.

Step-by-Step Solution:
Step 1: Convert the annual rate to decimal form. R = 8.5 percent = 8.5 / 100 = 0.085. Step 2: Convert the 90 day term to years using a 360 day year. T = 90 / 360 = 0.25 years. Step 3: Use the simple interest formula I = P * R * T. I = 8,000 * 0.085 * 0.25. Step 4: Compute intermediate product: 8,000 * 0.085 = 680 dollars per year. Step 5: Apply the time fraction: I = 680 * 0.25 = 170 dollars.

Verification / Alternative check:
An alternative check is to note that 0.25 of a year is exactly three months. Annual interest on 8,000 at 8.5 percent is 680 dollars. One quarter of that amount corresponds to three months: 680 / 4 = 170 dollars. This is consistent with the time calculation based on 90 days out of 360 and confirms the accuracy of the interest computed.

Why Other Options Are Wrong:
Option $150 and option $160 are both less than the correct value and would correspond to either a lower rate or a shorter time than 90 days. Option $180 is higher than the correct interest and would imply either a slightly higher annual rate or a longer loan term. Only 170 dollars fits exactly with 8.5 percent per annum simple interest for a quarter of a year on 8,000 dollars.

Common Pitfalls:
Students sometimes divide by 365 instead of 360 when the question explicitly instructs them to use a 360 day year, which would give a slightly different result. Others mistakenly treat 90 days as 9 months or as 0.9 years. Always read carefully whether the problem specifies ordinary simple interest with 360 days and ensure that days are correctly converted to a fraction of a year before applying the formula.

Final Answer:
The ordinary simple interest on the 90 day loan is $170.