From simple to compound — same rate (10%) and time (2 years): The simple interest on a certain principal for 2 years at 10% per annum is ₹ 90. What is the corresponding compound interest for the same time and rate?

Introduction / Context:
This problem converts a known simple-interest outcome into compound interest (same rate and duration). First deduce the principal from SI, then compute CI using the compounding formula.

Given Data / Assumptions:

• SI over 2 years at 10% p.a. = ₹ 90
• Rate r = 10% = 0.10
• Time t = 2 years
• Principal P = ?

Concept / Approach:
Simple interest SI = P * r * t. Hence P = SI / (r * t). After getting P, compute CI via A = P * (1 + r)^t and CI = A − P.

Step-by-Step Solution:
P = 90 / (0.10 * 2) = 90 / 0.20 = ₹ 450A = 450 * (1.10)^2 = 450 * 1.21 = ₹ 544.50CI = A − P = 544.50 − 450 = ₹ 94.50

Verification / Alternative check:
Second-year uplift equals “interest on interest” = P * r^2 = 450 * 0.01 = ₹ 4.50; SI for 2 years would be ₹ 90; CI must therefore be ₹ 94.50 (consistent).

Why Other Options Are Wrong:
₹ 99 and ₹ 108 overstate compounding; ₹ 95.60 does not match exact (1.10)^2; ₹ 92.00 undercounts by ignoring second-year interest on interest.

Common Pitfalls:
Mistaking SI = P * r (forgetting time), or using 2 * 10% as a compounded rate rather than multiplying by (1.10)^2.

Final Answer:
₹ 94.50