Simple interest vs compound interest on Rs 10000 at 10% for 3 years

Question

Calculate simple interest and compound interest on Rs 10,000 at 10% per annum for 3 years. Find the difference between CI and SI.

Solution — Step by Step

SI = \frac{P \times R \times T}{100}

where P = Principal, R = Rate (%), T = Time (years)

Given: P = 10,000, R = 10%, T = 3 years

SI = \frac{10000 \times 10 \times 3}{100} = \frac{300000}{100} = \text{Rs } 3000

Amount (SI) = P + SI = 10000 + 3000 = Rs 13,000

In compound interest, the interest earned each year is added to the principal, and next year’s interest is calculated on this new (larger) principal.

Year 1: Interest = $\frac{10000 \times 10}{100}$ = Rs 1000 Amount at end of Year 1 = 10000 + 1000 = Rs 11,000

Year 2: Interest = $\frac{11000 \times 10}{100}$ = Rs 1100 Amount at end of Year 2 = 11000 + 1100 = Rs 12,100

Year 3: Interest = $\frac{12100 \times 10}{100}$ = Rs 1210 Amount at end of Year 3 = 12100 + 1210 = Rs 13,310

CI = 13310 − 10000 = Rs 3,310

A = P\left(1 + \frac{R}{100}\right)^T

CI = A - P

A = 10000\left(1 + \frac{10}{100}\right)^3 = 10000 \times (1.1)^3

$(1.1)^3 = 1.1 \times 1.1 \times 1.1 = 1.21 \times 1.1 = 1.331$

A = 10000 \times 1.331 = \text{Rs } 13310

CI = 13310 - 10000 = \text{Rs } 3310

This confirms our year-by-year calculation.

\text{Difference} = CI - SI = 3310 - 3000 = \textbf{Rs 310}

This extra Rs 310 in CI comes from “interest on interest” — the interest earned in Year 1 and Year 2 also earns interest in subsequent years.

Why This Works

In simple interest, the base (principal) stays the same each year, so the interest is the same every year: Rs 1000/year → total = Rs 3000.

In compound interest, the base grows each year because previous interest is added. So:

Year 1 interest: Rs 1000 (on Rs 10,000)
Year 2 interest: Rs 1100 (on Rs 11,000)
Year 3 interest: Rs 1210 (on Rs 12,100)

The difference of Rs 310 is literally “interest on the interest”:

Rs 100 (10% of Year 1 interest Rs 1000, earned in Year 2)
Rs 100 (10% of Year 1 interest Rs 1000, earned in Year 3)
Rs 110 (10% of Year 2 interest Rs 1100, earned in Year 3)

Total = Rs 310. This is why compound interest grows exponentially over long periods.

Alternative Method — Shortcut Formula for CI − SI (2 years and 3 years)

For 2 years: $CI - SI = P \times \left(\frac{R}{100}\right)^2$

For 3 years: $CI - SI = P \times \left(\frac{R}{100}\right)^2 \times \left(3 + \frac{R}{100}\right)$

For 3 years at R = 10%, P = 10,000:

CI - SI = 10000 \times (0.1)^2 \times (3 + 0.1) = 10000 \times 0.01 \times 3.1 = 100 \times 3.1 = \text{Rs } 310

Same answer — and much faster for board exam time pressure.

The 2-year shortcut $CI - SI = P(R/100)^2$ is worth memorising for CBSE and competitive exams. It saves writing out year-by-year calculations entirely.

Common Mistake

Students often compute CI using SI formula (adding the same Rs 1000 each year) and get Rs 3000 as CI too. Always remember: in CI, interest is recalculated on the increased principal each year. The defining feature of compound interest is that interest earns interest.

Question

Solution — Step by Step

Why This Works

Alternative Method — Shortcut Formula for CI − SI (2 years and 3 years)

Common Mistake

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