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

Introduction / Context:
This question requires you to compute the simple interest on a loan taken for a fraction of a year and then determine the total repayment amount. It highlights the importance of converting months into years properly when using annual interest rates, a common theme in personal finance and aptitude examinations.

Given Data / Assumptions:

• Principal, P = $15,000.
• Annual simple interest rate, R = 7% per annum.
• Time period, T = 7 months.
• Interest is simple, not compounded.

Concept / Approach:
The simple interest formula is:
SI = (P * R * T) / 100Since R is per annum, we must express T in years. Seven months is a fraction of a year. After finding SI, we compute the total amount to be repaid using:
Amount, A = P + SI

Step-by-Step Solution:
Step 1: Convert time to years.T = 7 months = 7 / 12 yearsStep 2: Apply the simple interest formula.SI = (15000 * 7 * (7 / 12)) / 100Step 3: Simplify by combining the numeric factors.SI = (15000 * 7 * 7) / (12 * 100)SI = (15000 * 49) / 1,20015000 * 49 = 735,000SI = 735,000 / 1,200 = 612.50Step 4: Compute the total amount to be repaid.A = P + SI = 15,000 + 612.50 = $15,612.50

Verification / Alternative check:
Another way is to first find interest for one year, then multiply by the fraction 7 / 12. Interest for 1 year at 7% is (15000 * 7) / 100 = $1,050. Interest for 7 months is 1,050 * (7 / 12) = 1,050 * 0.5833..., which equals approximately $612.50. Adding this to the principal gives $15,612.50, confirming the previous result.

Why Other Options Are Wrong:

• $14,612.50 is less than the principal and would mean negative interest, which is not the case here.
• $13,612.50 is even lower and clearly impossible.
• $17,612.50 assumes a much higher interest amount than 7% per annum for 7 months.

Common Pitfalls:
Common mistakes include treating 7 months as 7 years or as 0.7 years instead of 7 / 12 years. Others forget to convert the percentage into a fraction by dividing by 100 or miscalculate the product 15000 * 49. Writing each step clearly and checking the size of the final interest against intuition (it should be much smaller than 7% of 15,000 for less than a year) helps avoid these errors.

Final Answer:
The interest due on the loan is $612.50, and the total amount that must be repaid is $15,612.50.