For a certain amount, the simple interest at 12 percent per annum for 6 years is Rs. 25920. On this same principal, what will be the compound interest for 2 years at 8 percent per annum, compounded annually, in this aptitude question on comparing simple and compound interest?

Introduction / Context:
This problem links simple interest and compound interest on the same principal. First, the principal is used with simple interest at a given rate and time to determine its value. Then, the same principal is invested at a different rate under compound interest for a shorter period. The task is to calculate the compound interest earned in the second scenario. Such chained questions are very common in quantitative aptitude tests and bank exams.

Given Data / Assumptions:

• Simple interest rate r₁ = 12 percent per annum.
• Time for simple interest t₁ = 6 years.
• Simple interest for this period is Rs. 25920.
• Same principal is then used for compound interest.
• Compound interest rate r₂ = 8 percent per annum.
• Time for compound interest t₂ = 2 years, compounded annually.

Concept / Approach:
First, we use the simple interest formula to find the principal P:
SI = (P * r₁ * t₁) / 100.
Once we know P, we apply the compound interest formula for 2 years at 8 percent per annum with annual compounding. The compound amount A is A = P * (1 + r₂/100)^t₂, and the compound interest CI is A − P. We then compare the computed value with the options provided.

Step-by-Step Solution:
Step 1: Let the principal be P. We are told that simple interest SI = 25920 at 12 percent for 6 years. Step 2: Use SI = (P * r₁ * t₁) / 100, so 25920 = (P * 12 * 6) / 100. Step 3: Simplify the denominator: 12 * 6 = 72, so 25920 = (72P) / 100. Step 4: Rearranging gives P = (25920 * 100) / 72 = 36000. Step 5: Now use compound interest for 2 years at 8 percent with P = 36000. Step 6: The amount after 2 years with annual compounding is A = P * (1 + 8/100)^2 = 36000 * (1.08)^2. Step 7: Compute (1.08)^2 = 1.1664, so A = 36000 * 1.1664 = 41990.4. Step 8: Compound interest CI = A − P = 41990.4 − 36000 = 5990.4. Step 9: Therefore, the compound interest for 2 years at 8 percent per annum is Rs. 5990.4.

Verification / Alternative check:
We can alternatively compute the compound interest directly using the formula CI = P * [(1 + r₂/100)^t₂ − 1]. With P = 36000, r₂ = 8, t₂ = 2, we get CI = 36000 * [(1.08)^2 − 1] = 36000 * (1.1664 − 1) = 36000 * 0.1664 = 5990.4. This matches the earlier calculation, confirming that our answer is consistent and correct.

Why Other Options Are Wrong:
Rs. 4326.3 and Rs. 5563.4 are lower than the correct interest and result from miscalculating the squared factor or mistakenly using one year instead of two. Rs. 5888.6 is close, but still incorrect, typically arising from rounding errors or approximating (1.08)^2 inaccurately. Rs. 6200.0 overshoots the correct amount and would correspond to a higher effective rate or misapplied principal. Only Rs. 5990.4 matches the exact computation of compound interest for the given data.

Common Pitfalls:
Some students incorrectly reuse the simple interest rate or time when computing the compound interest, or they forget to first find the principal from the simple interest information. Another error is to use 2 * 8 = 16 percent directly on the principal as if it were simple interest instead of using the compound factor (1.08)^2. Rounding (1.08)^2 too aggressively can also produce wrong answers close to, but not exactly, 5990.4. Careful step-by-step calculations help avoid these mistakes.

Final Answer:
The compound interest earned on the same principal for 2 years at 8 percent per annum, compounded annually, is Rs. 5990.4.