The only real difference between the two is whether interest itself earns further interest. Decide simple or compound first, and the correct formula becomes obvious.
Simple interest
SI = P × R × T / 100, and Amount = P + SI. Each year adds the same fixed amount.
Compound interest
Amount = P × (1 + R/100)^T, and CI = Amount − P. Each year's interest joins the principal and earns more.
How to Approach It
- Read SI versus CI — simple interest adds the same amount every year; compound interest grows because each year's interest joins the principal. The wording tells you which applies.
- Apply the formula cleanly — SI is PRT/100; the compound amount is P(1 + R/100)^T. For compound, find the amount first, then subtract the principal.
- Adjust for the compounding period — if interest compounds half-yearly, halve the rate and double the periods. Quarterly follows the same logic.
- Use the two-year shortcut — for exactly two years, the gap between CI and SI is P(R/100)^2, saving you from computing both in full.
Techniques & Methods
- SI is linear — each year's interest is identical, P×R/100. e.g. 5000 at 8% → 400 every year.
- CI as a multiplier — Amount = P(1 + R/100)^T; subtract P for the interest. e.g. 1000 at 10% for 2 years → ×1.21.
- CI − SI in 2 years — the gap equals P×(R/100)^2. e.g. 10000 at 10% → Rs 100.
- Half-yearly adjust — halve the rate and double the number of periods. e.g. 10% p.a. for 1 year → 5% for 2 periods.
The Edge
For 2 years, the gap between compound and simple interest is exactly P × (R/100)^2 — the interest-on-interest of year one. On Rs 10000 at 10% the 2-year difference is 10000 × 0.01 = Rs 100, computed without finding either interest in full.Worked example
Find the simple interest on Rs 5000 at 8% per annum for 3 years.
- Simple interest is the same amount every year, so the formula is just principal × rate × time ÷ 100.
- Substitute the values: 5000 × 8 × 3 ÷ 100.
- Work the top first: 5000 × 8 = 40,000, then × 3 = 120,000.
- Divide by 100: 120,000 ÷ 100 = 1200.
Answer: SI = Rs 1200
Worked example
Find the difference between CI and SI on Rs 8000 at 5% for 2 years.
- For exactly two years there is a shortcut for the gap between compound and simple interest: it equals P × (R/100)².
- It works because the only extra that CI earns is the second-year interest on the first year's interest.
- Plug in: 8000 × (5/100)² = 8000 × (0.05)² = 8000 × 0.0025.
- That gives 20, so compound interest exceeds simple interest by Rs 20 over the two years.
Answer: Difference = Rs 20
Worked Drills
Worked example
A sum doubles in 8 years at simple interest. It will triple in:
- Doubling means interest = P in 8 years, so the rate is 100/8 = 12.5%.
- Tripling means interest = 2P, which takes twice as long.
- Time = 16 years.
Answer: b) 16 years
Worked example
The compound interest on a sum for 2 years at 10% is Rs 420. The simple interest for the same is:
- CI factor over 2 years at 10% adds 0.21P, so 0.21P = 420 → P = 2000.
- SI = 2000 × 10 × 2 / 100 = 400.
Answer: b) Rs 400
Worked example
The difference between CI and SI on a sum at 10% for 2 years is Rs 50. The sum is:
- Use the 2-year shortcut: P × (R/100)^2 = 50.
- P × (0.1)^2 = 50 → P × 0.01 = 50 → P = 5000.
Answer: c) Rs 5000
Worked example
A sum at 20% compound interest (annual) doubles in approximately:
- Doubling requires (1.2)^t = 2.
- Solving for t gives about 3.8 years.
Answer: a) 3.8 years
Worked example
At what rate of simple interest will Rs 1200 amount to Rs 1440 in 2 years?
- Interest earned = 1440 − 1200 = 240.
- 240 = 1200 × r × 2 / 100 → r = 10%.
Answer: b) 10%
Worked example
A sum becomes four times itself in 12 years at simple interest. The rate is:
- Four times means interest = 3P over 12 years.
- Rate = 3 × 100 / 12 = 25%.
Answer: b) 25%
Worked example
Rs 8000 at 10% per annum, compounded half-yearly for 1 year, amounts to:
- Half-yearly: halve the rate to 5% and double the periods to 2.
- Amount = 8000 × (1.05)^2 = 8820.
Answer: c) Rs 8820
Worked example
A sum at CI amounts to Rs 4840 in 2 years and Rs 5324 in 3 years. The rate is:
- The third-year multiplier is 5324/4840 = 1.10.
- So the rate is 10%.
Answer: b) 10%
⚠ Watch out
- In SI the principal never changes; in CI it grows every period.
- When interest is compounded half-yearly, halve the rate and double the periods.
- The CI vs SI shortcut P(R/100)^2 works only for exactly 2 years.
Takeaways
- Decide SI or CI from the wording before touching any formula.
- SI grows by a constant amount; CI grows by a constant multiplier (1 + R/100)^T.
- Halve the rate and double the periods for half-yearly (quarter the rate, quadruple periods for quarterly).
- The 2-year CI − SI gap is exactly P(R/100)^2 — a fast back-solve for P, R or the difference.