📘 Simple & Compound Interest – Quick Study Notes
(For Maharashtra Police Sub‑Inspector (SI) – Quantitative Aptitude)
1. What is Interest?
- Interest is the extra money you pay (or earn) for borrowing (or lending) money.
- Two main types: Simple Interest and Compound Interest.
2. Simple Interest (SI)
Analogy – Think of a flat tip added to a restaurant bill. The tip is the same no matter how many days you stay.
| Term | Meaning | Formula (SI) | Example |
|---|---|---|---|
| P | Principal – the original amount | SI = (P × r × t) ÷ 100 |
P = ₹1,000, r = 5 % per year, t = 2 years |
| r | Rate of interest (annual) | ||
| t | Time (in years) | ||
| SI | Simple Interest earned | SI = (1000 × 5 × 2) ÷ 100 = ₹100 |
Total amount to pay/receive
A = P + SI
Example: A = 1000 + 100 = ₹1,100
3. Compound Interest (CI)
Analogy – Like a snowball rolling downhill: it starts small but keeps getting bigger as it rolls.
| Term | Meaning | Formula (A) | Example |
|---|---|---|---|
| P | Principal – the original amount | A = P × (1 + r/100n)^(n×t) |
P = ₹1,000, r = 5 % per year, n = 1 (compounded yearly), t = 2 years |
| r | Rate of interest (annual) | ||
| n | How many times interest is added per year | ||
| t | Time (in years) | ||
| A | Final amount after interest | A = 1000 × (1 + 5/100)^2 = 1000 × 1.05² = ₹1,102.50 |
Compound Interest earned
CI = A – P
Example: CI = 1102.5 – 1000 = ₹102.50
4. Quick Steps to Solve Any Question
- Read the problem – Grab the numbers for P, r, t (and n if compounding).
- Simple Interest
- Use
SI = (P × r × t) ÷ 100. - Total = P + SI.
- Use
- Compound Interest
- Use
A = P × (1 + r/100n)^(n×t). - CI = A – P.
- Use
- Check units – Make sure time is in years; rate is per year.
5. Cheat‑Sheet (Quick Reference)
| Interest Type | Formula (Total) | Formula (Interest Earned) |
|---|---|---|
| Simple | A = P + (P × r × t) ÷ 100 |
SI = (P × r × t) ÷ 100 |
| Compound | A = P × (1 + r/100n)^(n×t) |
CI = A – P |
- n = 1 → Annual compounding
- n = 12 → Monthly compounding
- n = 4 → Quarterly compounding
6. Mini‑Practice Questions
| # | Question | How to solve | Answer |
|---|---|---|---|
| 1 | Borrow ₹2,000 for 3 years at 4 % simple interest. How much to repay? | Use SI formula → SI = (2000 × 4 × 3) ÷ 100 = ₹240 |
Total = 2000 + 240 = ₹2,240 |
| 2 | Invest ₹5,000 for 2 years at 6 % compounded yearly. Final amount? | Use A formula → A = 5000 × (1 + 6/100)^2 = 5000 × 1.06² = ₹5,630 |
Final amount = ₹5,630 |
| 3 | Same investment as Q2 but compounded monthly. Final amount? | n = 12 → A = 5000 × (1 + 6/100 ÷ 12)^(12×2) |