Find Principal from CI vs SI with Semiannual Compounding — 2-year horizon at 10% p.a. (half-yearly compounding): The difference between the compound interest (compounded every 6 months) and simple interest at 10% per annum over 2 years is ₹ 124.05. Find the principal.

Introduction / Context:When compounding frequency increases (semiannual here), the effective amount exceeds simple interest by a calculable margin. If this margin is given for a known horizon, we can back out the principal by comparing the two amount factors over the same time span.

Given Data / Assumptions:

• Nominal annual rate = 10%.
• Compounded half-yearly ⇒ per half-year rate = 10%/2 = 5%, number of periods over 2 years = 4.
• Simple interest over 2 years amount factor = 1 + rt = 1 + 0.10*2 = 1.20.
• Difference in interest (CI − SI) over 2 years = ₹ 124.05.

Concept / Approach:Amount with semiannual compounding: A_CI = P(1 + 0.05)^4. Amount with SI: A_SI = P(1.20). The difference in interest equals P[(1.05)^4 − 1] − P(0.20) = P[(1.05)^4 − 1.20]. Solve P from the given difference.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• ₹ 10000, ₹ 6000, ₹ 12000, ₹ 9000 do not satisfy the exact difference factor at 10% with semiannual compounding for 2 years.

Common Pitfalls:

• Using 10% per half-year instead of 5%.
• Subtracting principals instead of interest portions.

Final Answer:Rs. 8000.