A loan of $15,000 is taken out at 7% simple interest per annum and is to be repaid in full after 7 months; under simple interest, what interest is due and what total amount must be repaid at the end of 7 months?

Introduction / Context:
This loan question uses simple interest with time expressed in months. The borrower takes a loan of 15,000 dollars at a fixed annual interest rate and repays it after 7 months. The problem asks both for the interest due and the total repayment amount. It tests correct handling of time conversion and application of the simple interest formula to short term loans.

Given Data / Assumptions:
- Principal P = 15,000 dollars. - Annual simple interest rate R = 7 percent per annum. - Time = 7 months. - Simple interest is used; no compounding is mentioned. - Required quantities: interest due and total amount to be repaid.

Concept / Approach:
The simple interest formula SI = (P * R * T) / 100 requires T in years. Hence 7 months must be converted to years as 7 / 12 years. Once we have T in years, we compute SI, then add it to the principal to find the total amount repayable. The answer options show only total amounts, but we can easily report both interest and amount in the explanation.

Step-by-Step Solution:
Step 1: Convert 7 months to years: T = 7 / 12 years. Step 2: Identify P = 15,000 dollars, R = 7 percent, T = 7 / 12. Step 3: Use SI = (P * R * T) / 100. Step 4: Substitute: SI = (15,000 * 7 * (7 / 12)) / 100. Step 5: Compute 15,000 * 7 = 1,05,000. Step 6: Multiply by 7 to get 1,05,000 * 7 = 7,35,000. Step 7: Divide by 12: 7,35,000 / 12 = 61,250. Step 8: Divide by 100: SI = 61,250 / 100 = 612.50 dollars. Step 9: Compute total amount A = P + SI = 15,000 + 612.50 = 15,612.50 dollars.

Verification / Alternative check:
We can also find the interest per year first. For one full year, interest is (15,000 * 7 * 1) / 100 = 1,050 dollars. For 7 months, which is 7 / 12 of a year, interest is 1,050 * 7 / 12 = 1,050 * 0.5833, which is approximately 612.50 dollars. Adding this to the principal gives a total repayment of 15,612.50 dollars, confirming the calculation.

Why Other Options Are Wrong:
An amount of 14,612.50 dollars would imply negative interest, which is impossible at a positive rate. An amount of 13,612.50 dollars is even lower and does not reflect any interest at all. An amount of 17,612.50 dollars assumes far more interest than 7 percent for 7 months on 15,000 dollars. Only 15,612.50 dollars is consistent with the simple interest formula and given data.

Common Pitfalls:
Learners often forget to convert months to years and use T = 7 in the formula, leading to a grossly inflated interest. Another mistake is to miscalculate the fraction 7 / 12 or to round too early. Keeping the exact fraction until the final step yields the correct interest and total amount.

Final Answer:
The interest due is 612.50 dollars, and the total amount to be repaid is $15,612.50.