Q.Find the difference between the compound interest and the simple interest on ₹12,000 for 2 years at 5% per annum (compounded annually).

Compute SI and CI separately for the same $P$, $R$ and $T = 2$ years, then subtract; the gap should equal the shortcut $P\left(\dfrac{R}{100}\right)^2$.

Given: $P = 12000$, $R = 5\%$ p.a., $T = 2$ years, compounded annually.

Method 1 — compute SI and CI separately.

Simple interest: $SI = \dfrac{P \times R \times T}{100} = \dfrac{12000 \times 5 \times 2}{100} = 1200$.

Compound interest: $A = 12000(1.05)^2 = 12000 \times 1.1025 = 13230$, so $CI = 13230 - 12000 = 1230$.

Difference $= CI - SI = 1230 - 1200 = 30$. …

Forgetting that SI and CI are equal in the first year, so the whole difference comes from the second year. Al …