Simple and Compound Interest: Formulas and the Quick Difference Trick

Interest questions appear in almost every quantitative section. There are only two formulas to master.

Simple interest

SI = (P × R × T) ÷ 100

where P is principal, R is the annual rate in percent and T is time in years.

Example: P = 5000, R = 8%, T = 3 years. SI = 5000 × 8 × 3 ÷ 100 = 1200. Amount = 5000 + 1200 = 6200.

Compound interest

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

Example: P = 10000, R = 10%, T = 2 years. Amount = 10000 × 1.1 × 1.1 = 12100. CI = 2100.

Comparing the two

For the same 10000 at 10% for 2 years:

Type	Interest
Simple	2000
Compound	2100

Compound interest earns interest on interest, so it grows faster.

The difference shortcut

For 2 years, the difference between CI and SI is:

P × (R/100)²

Here 10000 × (0.10)² = 100, which matches 2100 − 2000.

Compounding half-yearly or quarterly

Divide the rate by the number of periods per year and multiply the number of years accordingly.

Example: 8% per year compounded half-yearly for 1 year = 4% for 2 periods.

Doubling time

A rough guide is the rule of 72: money doubles in about 72 ÷ R years at R% compound interest. At 8% that is about 9 years.

Common traps

1. Rate per year versus per period.
2. Mixing months and years. Convert time to years.
3. Forgetting to subtract P when asked for interest rather than amount.

Tips

• Use multipliers: 10% growth means multiply by 1.1.
• Memorise common results such as 1.1² = 1.21.
• Check that CI is larger than SI for T > 1.

Practice

Regular short practice makes these formulas quick and reliable.

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