Simple and Compound Interest
About 6 min · Quantitative Aptitude · English
Time worked out from the lesson's 416 words at 150 words a minute, plus a minute for each question.
This topic tests your understanding of how money grows over time under different compounding scenarios. Mastery requires comfort with basic formulas, the ability to handle fractional time periods, and familiarity with non-annual compounding (half-yearly, quarterly). Questions on installments and population/depreciation analogies also appear. The key to success is recognizing problem patterns quickly and applying the correct formula without calculation errors. Unlike more abstract topics, interest problems are highly formulaic—memorize the core equations and practice variations to build speed.
Key ideas
- Simple Interest grows linearly: Each year's interest is calculated only on the original principal, so SI = (P × R × T)/100. The total amount A = P + SI.
- Compound Interest grows exponentially: Each period's interest is added to the principal before calculating the next period's interest. The amount formula is A = P(1 + R/100)^n, where n is the number of compounding periods.
- Difference between SI and CI: For small time periods (2–3 years), the difference is small but predictable. For 2 years: CI − SI = P(R/100)². This shortcut speeds up comparison problems.
- Non-annual compounding: When interest compounds half-yearly, divide the annual rate by 2 and double the time in years. For quarterly compounding, divide rate by 4 and multiply time by 4.
- Rate and time adjustments: Always match the rate period to the time period. If rate is annual but compounding is half-yearly, convert both consistently.
Watch out for
- Confusing rate and time units: Applying a 10% annual rate directly to half-yearly compounding without halving the rate. Always convert rate and time to match the compounding frequency.
- Forgetting to subtract principal for CI: Calculating amount A correctly but forgetting CI = A − P. Many students write the amount as the final answer when CI is asked.
- Misapplying the difference formula: Using CI − SI = P(R/100)² for 3 years instead of 2 years. The shortcut formula for difference changes with the number of years.
Quick reference
- SI formula: SI = PRT/100; grows linearly each year.
- CI formula (annual): A = P(1 + R/100)^T; exponential growth.
- Half-yearly CI: halve rate, double time periods.
- Quarterly CI: divide rate by 4, multiply time by 4.
- CI − SI for 2 years: P(R/100)².
Check yourself: 3 questions
1. The simple interest on ₹2000 at 10% per annum for 3 years is:
2. The compound interest on ₹5000 at 10% per annum for 2 years (compounded annually) is:
3. A sum of money doubles itself in 8 years at simple interest. The rate of interest per annum is:
This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 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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