A sum of Rs. 1200 is lent to be repaid in 5 equal annual instalments of Rs. 264 each, where each instalment includes both principal and simple interest. Based on this repayment pattern, what is the annual rate of simple interest per annum?

Introduction / Context:
This question involves a loan that is repaid in equal annual instalments, each instalment including both principal and simple interest. We are given the original principal, the number of instalments, and the instalment amount, and we must determine the annual simple interest rate. The key idea is to recognize that the total of all instalments equals the principal plus the total simple interest over the full term.

Given Data / Assumptions:

• Principal P = Rs. 1200.
• Number of equal annual instalments n = 5.
• Each instalment = Rs. 264.
• Simple interest is charged at a constant rate R% per annum for 5 years on the original principal.
• Total interest I_total = P * R * n / 100 in the simple interest model for this question.

Concept / Approach:
The sum of the 5 instalments is the total amount repaid. This total equals the original principal plus the simple interest on that principal for the entire 5-year period. We can therefore find the total interest paid, then apply the simple interest formula I_total = (P * R * T) / 100 with T = 5 years to solve for R.

Step-by-Step Solution:
Total amount repaid over 5 years = 5 * 264 = Rs. 1320. Total interest paid I_total = total repaid - principal = 1320 - 1200 = Rs. 120. Under the simple interest model here, interest for 5 years on P is I_total = (P * R * 5) / 100. So 120 = (1200 * R * 5) / 100. Compute 1200 * 5 / 100 = 60, so equation becomes 120 = 60R. Therefore, R = 120 / 60 = 2% per annum.
Verification / Alternative check:
At a 2% simple interest rate on Rs. 1200 for 5 years, total interest should be I_total = 1200 * 2 * 5 / 100 = 1200 * 0.1 = Rs. 120, which matches the interest calculated from the instalments. Thus, the repayment schedule of five instalments totalling Rs. 1320 is consistent with a rate of 2% per annum on the original principal.

Why Other Options Are Wrong:
Rates of 3%, 4%, 5%, or 6% per annum would result in total interest values of 180, 240, 300, and 360 rupees respectively on Rs. 1200 over 5 years. Adding these interest amounts to the principal would yield total repayments different from Rs. 1320, contradicting the instalment information given in the problem.

Common Pitfalls:
A key pitfall is overcomplicating the problem by attempting to track interest on reducing balances for each year, which is more typical of reducing balance methods. The question, however, treats simple interest on the original principal for the entire period. Misinterpreting the model or forgetting to subtract the principal from the total of instalments before applying the formula can also lead to wrong answers.

Final Answer:
The annual rate of simple interest is 2% per annum.