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Compound Interest · Topic 3 of 6

⚖️ CI vs SI Difference

1 exam question type, fully solved

Simple interest stays flat — you earn the same amount every year. Compound interest earns “interest on interest”, so from the second year onward it always runs ahead of SI. That fixed lead is exactly what these questions test.

The CI − SI shortcut formulas

In year 1 both are identical. The gap opens in year 2, because CI now charges interest on the first year's interest as well. For a 2-year period that extra is exactly:

For a 3-year period a third slice is added, giving:

• Find P: drop the difference into the right formula and divide. At the 2-year gap is just , so (difference).

• Find R: the gap is the interest on the first year's interest, so .

• Trap: never use the 2-year formula on a 3-year sum — check the time first, because CI > SI pulls ahead faster than you expect.

📈CI vs SI Growth ChartInteractive
04k9k13k17kPY1Y2Y3Y4Y5SI (linear)CI (exponential)
CI is always > SI for T > 1 year. The gap widens exponentially — this is the power of “interest on interest.”
YearSI AmountCI AmountDifference
1₹11,000.00₹11,000.00—
2₹12,000.00₹12,100.00₹100.00
3₹13,000.00₹13,310.00₹310.00
4₹14,000.00₹14,641.00₹641.00
5₹15,000.00₹16,105.10₹1,105.10

At 10% for 2 years on ₹4,000, CI − SI = ₹.

📝Practice Questions

Q1For 2 years at 10% per annum, the difference between CI and SI on ₹6,000 is:

Q2The difference between CI and SI for 2 years at 5% per annum is ₹10. The sum is:

Q3The difference between CI and SI on a sum at 10% per annum for 3 years is ₹310. The sum is:

📚

Real exam questions — CI vs SI Difference

1 question types · 5 solved examples from real SSC papers

CI always beats SI once the time crosses one year, because compound interest earns interest on the interest already added. That fixed lead has clean shortcut formulas — learn them once and you can compute the gap, or work backwards to the principal or rate, in seconds.

How to solve this type
Simple interest is flat — the same amount is added every year. Compound interest charges “interest on interest”, so from year 2 onward it always runs ahead of SI. That lead has fixed formulas you should never re-derive under exam pressure.
For 2 years: CI−SI=P(R100)2\text{CI}-\text{SI}=P\left(\dfrac{R}{100}\right)^2 — this is exactly the interest earned on the first year's interest.
For 3 years: CI−SI=P(R100)2(3+R100)\text{CI}-\text{SI}=P\left(\dfrac{R}{100}\right)^2\left(3+\dfrac{R}{100}\right).
To find P, divide the given difference by the rate-factor; to find R, remember the gap is the interest on the first year's interest, so R=2(CI−SI)SI×100R=\dfrac{2(\text{CI}-\text{SI})}{\text{SI}}\times100. The one big trap is mixing the two formulas — always check the time period first.

Find the difference between CI and SI on ₹5,000 at 10% per annum for 3 years.

A₹165B₹155C₹175D₹160

The difference between CI and SI on a sum at 10% per annum for 3 years is ₹930. Find the sum.

A₹30,000B₹25,000C₹31,000D₹27,419

The difference between CI and SI on a sum at 10% per annum for 2 years is ₹50. Find the sum.

A₹7,000B₹5,000C₹4,000D₹6,000

The difference between CI and SI for 2 years at 8% per annum is ₹80. Find the principal.

A₹10,000B₹12,500C₹11,500D₹15,000

For a certain sum, CI for 2 years is ₹510 and SI for 2 years at the same rate is ₹500. Find the rate.

A4%B5%C8%D6%