UP Police Constable · Bite-size lessons
Simple and Compound Interest
About 6 min · Numerical & Mental Ability · English
Time worked out from the lesson's 420 words at 150 words a minute, plus a minute for each question.
The formulas in this topic are straightforward. Mastering Simple Interest (SI) and Compound Interest (CI) — especially compounding annually and half-yearly — is essential. Additionally, instalment-based questions test whether you can apply interest formulas in multi-step scenarios. Unlike topics requiring lengthy calculations, interest problems can be solved quickly if you know the core formulas and can identify which one applies. Focus on recognising the problem type, selecting the right formula, and executing calculations accurately within exam time constraints.
Key ideas
- Simple Interest (SI) — Interest calculated only on the original principal throughout the loan/investment period. The interest amount stays the same every year.
- Compound Interest (CI) — Interest calculated on principal plus accumulated interest from previous periods. The interest amount increases each period.
- Principal (P) — The initial amount borrowed or invested.
- Rate (R) — Annual interest rate expressed as a percentage per annum.
- Time (T) — Duration of the loan or investment, typically in years. For half-yearly compounding, adjust both rate and time.
Watch out for
- Confusing SI and CI formulas — Students often use SI formula for CI problems or vice versa. Always check whether the problem mentions "compound" or just "interest" (usually means SI unless stated otherwise). → Read the question carefully; "compound" is the keyword.
- Forgetting to adjust for half-yearly compounding — Many students use the annual CI formula even when compounding is half-yearly or quarterly. → Remember: half-yearly means R/2 and 2T; quarterly means R/4 and 4T.
- Using T in months or days without conversion — If time is given in months or days, convert to years (months/12 or days/365) before applying the formulas. → Always standardise T to years unless otherwise specified.
Quick reference
- SI = PRT/100; Amount = P + SI
- CI (annual): A = P(1 + R/100)^T; CI = A – P
- CI (half-yearly): Use R/2 and 2T in the formula
- CI – SI (2 years) = P(R/100)²; saves calculation time
- For instalments: discount each payment back to present value using (1 + R/100)^n
Check yourself: 3 questions
1. A sum of Rs 8000 is invested at 10% simple interest per annum. What will be the total amount after 3 years?
2. A person borrows Rs 12,000 at 8% compound interest per annum. If the interest is compounded annually, what will be the amount after 2 years?
3. A sum of Rs 20,000 is invested at 12% per annum compound interest, compounded half-yearly. What will be the compound interest after 1 year?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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