Simple & Compound Interest – Quick Study Notes
(For Tamil Nadu Patwari / Lekhpal – Quantitative Aptitude)
1. Why Do We Need These Notes?
- These notes are tiny, clear and use everyday language.
- They help you solve quick questions in exams.
- No heavy math – just a few short steps.
2. Simple Interest (SI)
| Concept | Everyday Analogy | Formula (in plain words) |
|---|---|---|
| What it is | Money grows like a plant that only gets one set of leaves each year. | SI = Principal × Rate × Time ÷ 100 |
| Principal (P) | The amount you start with (the seed). | – |
| Rate (R) | How many percent the plant grows each year. | – |
| Time (T) | How many years the plant stays in the soil. | – |
| Interest (SI) | The extra leaves you collect after all the years. | – |
Tiny Example
- P = ₹1,000
- R = 5 % per year
- T = 2 years
SI = 1000 × 5 × 2 ÷ 100
SI = 1000 × 10 ÷ 100
SI = 100
Answer: After 2 years you get ₹100 extra.
Total amount = ₹1,000 + ₹100 = ₹1,100.
3. Compound Interest (CI)
| Concept | Everyday Analogy | Formula (in plain words) |
|---|---|---|
| What it is | The plant now gets a second set of leaves that also grow each year (interest on interest). | CI = P × (1 + R/100)ⁿ – P |
| n | Number of times interest is added (usually once a year). | – |
Tiny Example
- P = ₹1,000
- R = 5 % per year
- n = 2 years
CI = 1000 × (1 + 5/100)² – 1000
CI = 1000 × (1.05)² – 1000
CI = 1000 × 1.1025 – 1000
CI = 1102.50 – 1000
CI = 102.50
Answer: After 2 years you get ₹102.50 extra.
Total amount = ₹1,000 + ₹102.50 = ₹1,102.50.
4. Quick Tips for the Exam
| Tip | Why it Helps |
|---|---|
| Use 1 % trick | 1 % of ₹1000 = ₹10. So 5 % = 5 × 10 = ₹50. |
| Remember “÷ 100” | After multiplying P × R × T, just move the decimal two places left. |
| For CI, round early | After each year, round the interest to the nearest rupee if the exam allows. Easier mental math. |
| Write the steps | Even if you’re quick, writing the short steps keeps you from missing a number. |
| Check units | Rate is per year, time is in years. If you see months, convert to years first. |
5. Mini‑Practice Problems
-
Simple Interest
- P = ₹2,000, R = 3 %, T = 4 years.
- What is the total amount?
-
Compound Interest
- P = ₹5,000, R = 4 % per year, compounded yearly, for 3 years.
- What is the total amount?
(Try to solve using the tips above before checking the answers.)
6. Answers (Check After You Try)
| Problem | Steps | Result |
|---|---|---|
| 1. SI | SI = 2000 × 3 × 4 ÷ 100 = 2000 × 12 ÷ 100 = 240 |
Total = ₹2,240 |
| 2. CI | (1 + 4/100)³ = 1.04³ = 1.124864 → CI = 5000 × 1.124864 – 5000 = 5624.32 – 5000 = 624.32 |
Total ≈ ₹5,624.32 |
7. Final Checklist Before the Exam
- Know the difference: simple grows once a year, compound grows on growth.
- Keep the formula handy:
SI = P × R × T ÷ 100andCI = P × (1 + R/100)ⁿ – P. - Practice the 1 % trick for quick multiplication.
- When in doubt, write a quick step‑by‑step line.
Good luck,