Simple & Compound Interest

Interest questions test the same underlying idea as Profit & Loss — growth over a base value — but now that growth happens over time.

Simple Interest (SI)

SI = (P × R × T) / 100, where P = Principal, R = Rate % per annum, T = Time in years. Amount = P + SI.

Compound Interest (CI)

Amount = P × (1 + R/100)ᵀ. CI = Amount − P.

For 2 years, a useful shortcut: CI − SI = P × (R/100)².

Worked Example 1

UdaanPath sets aside a ₹5,000 scholarship fund at 8% simple interest per annum for 3 years before awarding it. Find the interest earned.

SI = (5000 × 8 × 3) / 100 = ₹1,200.

Worked Example 2

Find the CI on ₹10,000 at 10% per annum for 2 years, compounded annually.

Amount = 10000 × (1.1)² = 10000 × 1.21 = ₹12,100. CI = 12100 − 10000 = ₹2,100.

Worked Example 3

Find the difference between CI and SI on ₹8,000 at 5% per annum for 2 years.

Using the shortcut: Difference = 8000 × (5/100)² = 8000 × 0.0025 = ₹20.

Common mistakes

For compound interest with a time period in months (e.g. "compounded half-yearly"), remember to halve the rate and double the number of periods before applying the formula — using annual R and T directly gives a wrong answer.

Practice Set

1. Find the SI on ₹12,000 at 6% per annum for 4 years.
2. Find the CI on ₹15,000 at 10% per annum for 2 years.
3. A sum becomes double in 8 years at simple interest. Find the rate of interest.
4. Find the CI on ₹20,000 for 1 year at 10% per annum, compounded half-yearly.