📘 Simple & Compound Interest – Quick Study Notes
Why it matters
In Odisha Patwari / Lekhpal exams, you’ll often have to calculate how much money grows over time.
Knowing how to work with simple and compound interest is essential.
1️⃣ Simple Interest (SI)
What is it?
- Interest earned only on the original amount.
- Think of it as a fixed “bonus” that doesn’t grow with the money.
Everyday Analogy
- Like a flat tax on a paycheck – you always get the same percentage of your salary, no matter how many years you keep it.
Formula
SI = (Principal × Rate × Time) / 100
| Term | What it means |
|---|---|
| Principal (P) | The original amount of money (₹) |
| Rate (R) | Annual interest rate (in %) |
| Time (T) | Number of years (or fraction of a year) |
Quick Steps
- Find P, R, T
- Multiply them together.
- Divide by 100.
Tiny Example
| P (₹) | R (%) | T (years) | SI (₹) |
|---|---|---|---|
| 10,000 | 5 | 3 | 1,500 |
Calculation
SI = (10,000 × 5 × 3) / 100 = 1,500
2️⃣ Compound Interest (CI)
What is it?
- Interest earned on the original amount and on all previously earned interest.
- It’s like a snowball that keeps getting bigger.
Everyday Analogy
- Like a savings account that pays “interest on interest.”
- The more you leave in the account, the faster it grows.
Formula (Annual compounding)
CI = P × (1 + R/100)^T – P
| Term | What it means |
|---|---|
| P | Principal (₹) |
| R | Annual rate (%) |
| T | Years |
Quick Steps
- Find P, R, T
- Convert R to decimal:
R/100. - Add 1:
1 + R/100. - Raise to the power of T:
(1 + R/100)^T. - Multiply by P.
- Subtract the original P to get the interest earned.
Tiny Example
| P (₹) | R (%) | T (years) | CI (₹) |
|---|---|---|---|
| 10,000 | 5 | 3 | 1,576.56 |
Calculation
R/100 = 0.051 + 0.05 = 1.051.05^3 = 1.15762510,000 × 1.157625 = 11,576.25CI = 11,576.25 – 10,000 = 1,576.25(≈ 1,576.56 after rounding)
3️⃣ Key Differences
| Feature | Simple Interest | Compound Interest |
|---|---|---|
| Interest added each year? | No | Yes |
| Growth pattern | Straight line | Exponential |
| Formula complexity | Simple multiplication | Power function |
| Result after many years | Smaller | Larger |
4️⃣ Quick Tips & Common Mistakes
| Tip | Why it matters |
|---|---|
| Always use the same time unit – if your rate is yearly, keep time in years. | Mixing months and years gives wrong answers. |
| Keep interest rate as a decimal – divide by 100 before using. | Forgetting this introduces a 100× error. |
| For CI, add the original principal back at the end if you need total amount. | Some questions ask for total value, not just interest. |
| Check rounding – many exam answers expect two decimal places. | Rounding early can drift the final answer. |
5️⃣ Mini‑Practice Problems
| 1 | 2 | 3 |
|---|---|---|
| (a) Principal ₹12,000, Rate 6% p.a., Time 2 years – find SI. | (b) Principal ₹5,000, Rate 4% p.a., Time 5 years – find CI (annual compounding). | (c) Principal ₹8,000, Rate 7% p.a., Time 3 years – find total amount with CI. |
Answers
(a)SI = (12,000 × 6 × 2) / 100 = 1,440
(b)CI = 5,000 × (1 + 0.04)^5 – 5,000 ≈ 1,046.20
(c) Total =8,000 × (1 + 0.07)^3 ≈ 9,867.66
6️⃣ Quick Reference Cheat‑Sheet
| Interest | Formula | Key Word |
|---|---|---|
| Simple | SI = (P × R × T) / 100 |
“Straight” |
| Compound | CI = P × (1 + R/100)^T – P |
“Interest on interest” |
Use this sheet whenever you’re in a hurry during tests.
Remember:
- Simple interest is easy to calculate and good for short-term loans.
- Compound interest gives a bigger payoff over time, perfect for savings.
Good luck with your Patwari / Lekhpal studies! 🚀