On a certain principal, the simple interest for 2 years is Rs. 4800, whereas the compound interest on the same principal for the same 2 years is Rs. 5088. Based on this difference between simple and compound interest over 2 years, what is the annual rate of interest (in percent)?

Introduction / Context:
This question compares simple interest and compound interest on the same principal over the same period of 2 years. Because compound interest adds interest on interest, it is slightly higher than simple interest for the same rate and time. The difference between the amounts of simple and compound interest allows us to determine the underlying annual rate of interest.

Given Data / Assumptions:

• Simple interest for 2 years on principal P is Rs. 4800.
• Compound interest for 2 years on the same P is Rs. 5088.
• Time T = 2 years in both cases.
• Rate R is the same in both cases and is to be found.
• Simple interest formula: SI = (P * R * T) / 100.
• Compound amount for 2 years: A = P * (1 + R / 100)^2, and CI = A - P.

Concept / Approach:
From the simple interest, we can relate P and R. From the compound interest, we relate P and R in another way. Solving these two relations together yields both P and R. However, we do not need to explicitly know P to find R; we can use the equations strategically to solve for R directly.

Step-by-Step Solution:
From simple interest: SI = 4800 = P * R * 2 / 100. So P * R = 4800 * 100 / 2 = 240000. From compound interest: CI = 5088 = P * [(1 + R / 100)^2 - 1]. Let k = R / 100. Then (1 + k)^2 - 1 = 2k + k^2. Thus, 5088 = P * (2k + k^2). We also know P * k = P * R / 100 = (P * R) / 100 = 240000 / 100 = 2400. So express 5088 as P * (2k + k^2) = P * 2k + P * k^2 = 2 * 2400 + P * k^2. This gives 5088 = 4800 + P * k^2, so P * k^2 = 288. But P * k^2 = (P * k) * k = 2400 * k, so 2400 * k = 288. Therefore k = 288 / 2400 = 0.12, so R = 0.12 * 100 = 12 percent per annum.
Verification / Alternative check:
Using R = 12% and P from P * R = 240000, we get P = 240000 / 12 = 20000. Simple interest for 2 years: SI = 20000 * 12 * 2 / 100 = 4800, as given. Compound amount for 2 years: A = 20000 * (1.12)^2 = 20000 * 1.2544 = 25088, so CI = 25088 - 20000 = 5088, matching the question. This confirms R = 12%.

Why Other Options Are Wrong:
Rates of 6 percent, 10 percent, 18 percent, or 24 percent produce different relationships between SI and CI and do not lead to a simple interest of 4800 and compound interest of 5088 on the same principal in 2 years. When substituted, the differences between SI and CI are either too large or too small.

Common Pitfalls:
One common mistake is to assume that the difference between CI and SI over 2 years is simply P * (R / 100)^2, but misapplying this can cause algebra errors. Others try random substitution of rates without using the given SI value to form equations. Systematically using both interest expressions keeps the work clear and accurate.

Final Answer:
The annual rate of interest is 12 percent per annum.