Simple and Compound Interest Comparison: In 2 years at simple interest, a principal amount increases by 8% in total. At the same annual rate, compounded annually, what will be the compound interest (in ₹) earned on ₹10,00,000 in 2 years?

Introduction / Context:
This problem links simple interest (SI) information with compound interest (CI) at the same rate. You are told how much a principal grows over 2 years under simple interest and then asked to find the compound interest on a specific principal over the same period and rate. This is a classic aptitude question that checks whether you can switch between SI and CI correctly.

Given Data / Assumptions:

• Under simple interest, a principal increases by 8% in 2 years.
• Principal for the CI calculation = ₹10,00,000.
• Time for CI = 2 years.
• Compounding is annual.
• Rate of interest is the same in both cases.

Concept / Approach:
If a sum increases by 8% in 2 years under simple interest, that means the total SI in 2 years is 8% of the principal. For SI, SI = (P * r * t) / 100, so over 2 years the effective increase is 2r%. Therefore, 2r = 8, giving r = 4% per annum. Once we know r, we can compute CI on ₹10,00,000 using the compound interest formula with annual compounding for 2 years: Amount A = P * (1 + r / 100)^2, CI = A - P.

Step-by-Step Solution:
Step 1: From SI information, total increase in 2 years = 8% of the principal. Step 2: Under SI, effective 2 year increase = 2r%. So 2r = 8. Step 3: Solve for r: r = 8 / 2 = 4% per annum. Step 4: For CI, principal P = ₹10,00,000 and time t = 2 years at r = 4% compounded annually. Step 5: Compute amount A: A = P * (1 + r / 100)^2 = 10,00,000 * (1.04)^2. Step 6: (1.04)^2 = 1.0816, so A = 10,00,000 * 1.0816 = ₹10,81,600. Step 7: Compound interest CI = A - P = 10,81,600 - 10,00,000 = ₹81,600. Step 8: Therefore, the CI earned is ₹81,600.

Verification / Alternative check:
You can verify quickly by observing that for 4% per annum, SI for 2 years would be 8% of ₹10,00,000, that is ₹80,000. CI must be slightly greater than SI because interest also earns interest in the second year. The computed CI of ₹81,600 is just a bit more than ₹80,000, which is logically consistent.

Why Other Options Are Wrong:

• ₹90,000: This is too high and would require a rate higher than 4%.
• ₹86,000: Also larger than the correct CI, not matching 4% compounded for 2 years.
• ₹94,000: Much too high for only 4% per annum over 2 years.
• ₹80,000: This equals the 2 year simple interest, not the compound interest, so it ignores compounding.

Common Pitfalls:
Many learners mistakenly treat the 8% increase as an annual rate instead of the 2 year increase, which would give r = 8% instead of 4%. Others compute simple interest again instead of using the compound interest formula. Always interpret the time period carefully and choose the correct formula (SI or CI) for the quantity being asked.

Final Answer:
The compound interest on ₹10,00,000 for 2 years at the same rate is ₹81,600.