Simple and Compound Interest
About 6 min · Everyday Mathematics · English
Time worked out from the lesson's 410 words at 150 words a minute, plus a minute for each question.
Simple and Compound Interest is a high-scoring topic in SOF IMO that connects everyday banking and finance with mathematical computation. Students must master the formulas for SI and CI, understand the difference between them, and solve multi-step word problems involving principal, rate, time, and amount. This topic can appear in the Everyday Mathematics section and in the Achievers Section when combined with other concepts like profit-loss or time-work.
Key ideas
- Simple Interest (SI) is calculated only on the original principal for the entire period. The interest earned each year remains constant.
- Compound Interest (CI) is calculated on the principal plus accumulated interest from previous periods. Money "grows on itself," leading to exponential growth.
- Amount (A) is the total sum returned at the end of the period: Amount = Principal + Interest.
- Rate (R) is always expressed as a percentage per annum unless stated otherwise (half-yearly, quarterly compounding changes the effective rate).
- Time (T) is measured in years unless specified otherwise. For half-yearly compounding, double the time and halve the rate; for quarterly, quadruple the time and quarter the rate.
Watch out for
- Confusing SI and CI formulas → Always check if interest is simple or compound. If not mentioned, assume compound for real-world banking scenarios; simple for straightforward loan problems.
- Forgetting to subtract principal to find CI → CI = A – P. Students often report the amount as the interest itself.
- Incorrect handling of half-yearly/quarterly compounding → Remember: double the periods and halve the rate for half-yearly; quadruple periods and quarter the rate for quarterly. Don't just plug in original R and T.
Quick reference
- SI grows linearly; CI grows exponentially — CI always exceeds SI for T > 1.
- For 2-year difference: CI – SI = P(R/100)² — useful for finding P or R quickly.
- Half-yearly compounding: double time, halve rate → A = P(1 + R/200)^(2T).
- Instalment present value = Instalment / (1 + R/100)^time — sum these to equal principal.
- If rate or time not given, use CI – SI difference formulas or algebraic setup.
Check yourself: 3 questions
1. A person borrows Rs 15000 at 10% per annum compound interest. If the interest is compounded annually, what amount will he have to pay back after 2 years?
2. What sum will amount to ₹7260 in 2 years at 10% per annum compound interest, compounded annually?
3. At what rate percent per annum will ₹4000 amount to ₹5000 in 2 years at simple interest?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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