Compound Interest · Topic 1 of 6

🌱 CI Basics & Finding the Principal

2 exam question types, fully solved

You lend or borrow a sum of money called the principal (P). The bank adds interest at a yearly rate (R%). With compound interest each year's interest is added back, so the next year earns interest on the interest too. The total you end with is the amount (A), and the interest is just.

The one formula, and three faster ways to use it

Core formula: after years, , then . Unlike simple interest you do not add the rate up each year — the base keeps growing.

• 2-year net-effect shortcut: for exactly 2 years the whole CI works out to one effective rate of the principal. So 10% over 2 yr ; just take 21% of P in one go.

• Ratio / multiplier method: turn the rate into a fraction — 5% , 10% , 20% . Multiply once per year. Handy results: 10% over 2 yr = +21%, over 3 yr = +33.1% .

• Find the Principal: the amount is P already multiplied by , so to get P back you divide the amount by that multiplier — never subtract the interest. E.g. ₹9,680 at 10% for 2 yr gives .

Sanity check: CI is always a touch more than the simple interest. If your answer equals the SI, you forgot the “interest on interest”.

📈CI vs SI Growth ChartInteractive

Principal (₹)Rate (% p.a.)Years (T) — 5

CI is always > SI for T > 1 year. The gap widens exponentially — this is the power of “interest on interest.”

Year	SI Amount	CI Amount	Difference
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

For 10% over 2 years the effective rise is 21%, so the CI on ₹1,000 is ₹.

Q1The compound interest on ₹5,000 at 10% per annum for 2 years (compounded annually) is:

Q2A sum amounts to ₹9,680 in 2 years at 10% per annum compound interest. The principal is:

Q3The compound interest on ₹4,000 at 5% per annum for 2 years (compounded annually) is:

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Real exam questions — CI Basics & Finding the Principal

2 question types · 7 solved examples from real SSC papers

These are real SSC questions on the core CI engine: grow a sum with $A=P\left(1+\dfrac{R}{100}\right)^T$ , read off $CI=A-P$ , and run it backwards to find the principal. Every solution uses the 2-year net-rate shortcut or a clean multiplier instead of long powers — tap to reveal.

How to solve this type

Never add the rate up like simple interest — each year earns interest on the previous year's interest. For 2 years use the effective CI rate

2R+\dfrac{R^2}{100}\%

and take that percent of the principal in one shot. For neat rates switch to a multiplier: 5%

=\dfrac{21}{20}

, 10%

=\dfrac{11}{10}

, so 10% over 2 yr = +21%, over 3 yr = +33.1%. CI is always a little MORE than the simple interest — if your answer equals the SI, you forgot the interest-on-interest.

Find the compound interest on ₹8,000 at 10% per annum for 2 years, compounded annually.

A₹1,680B₹1,600C₹1,760D₹1,800

A sum of ₹8,000 is lent at 5% per annum compound interest for 2 years. Find the compound interest.

A₹820B₹780C₹840D₹800

What is the compound interest on ₹4,000 at 15% per annum for 2 years, compounded annually?

A₹1,200B₹1,320C₹1,245D₹1,290

A sum of ₹10,000 is invested at 10% per annum compound interest for 3 years. Find the amount.

A₹13,500B₹13,100C₹13,310D₹13,000