Compound Interest and the CI–SI Difference

Compound interest

Interest is added to the principal at the end of each period, and the next period's interest is calculated on this new amount.

A = P(1 + R/100)ⁿ, CI = A − P

Example: ₹10,000 at 10% for 2 years → 10000 × 1.1 × 1.1 = 12,100 → CI = ₹2,100.

Half-yearly / quarterly compounding

• Half-yearly: rate = R/2, periods = 2n.
• Quarterly: rate = R/4, periods = 4n.

Example: ₹10,000 at 20% p.a. compounded half-yearly for 1 year → 10% for 2 periods → ₹12,100.

CI − SI difference (shortcuts)

• 2 years: D = P(R/100)². ₹5,000 at 10% → 5000 × 0.01 = ₹50.
• 3 years: D = P(R/100)²(3 + R/100).

Multiplying pattern

If a sum becomes 2 times in 5 years at CI, it becomes 4 times in 10 years and 8 times in 15 years (powers of 2).

Exam tips (RRB NTPC)

1. For 2–3 years, successive percentage (10% then 10% = 21%) is fastest.
2. CI and SI are equal for the first year.

Analogy

Compound interest is like a snowball rolling downhill. It picks up snow not only from the ground but on top of the snow it already gathered, so it grows faster every turn. Simple interest is a snowman built by adding the same scoop each day — steady, but never accelerating.