Simple & Compound Interest – Study Notes
(Karnataka Forest Guard – Quantitative Aptitude)
1. Simple Explanation
| Concept | What it means | When it is used? |
|---|---|---|
| Simple Interest (SI) | Interest calculated only on the principal amount. | Short‑term loans, bank deposits (sometimes), everyday calculations. |
| Compound Interest (CI) | Interest calculated on the principal and on previously earned interest. | Long‑term investments, savings accounts, loans with compounding, mortgages. |
Rule of thumb – If the problem says “interest is added to the principal” or “interest is earned on interest”, it’s compound.
2. Key Formulae
| Variable | Symbol | Definition |
|---|---|---|
| Principal | (P) | Initial amount of money |
| Rate of interest | (r) | Nominal yearly rate (in %). Use (r = \frac{\text{rate%}}{100}) in formulas. |
| Time | (t) | Number of years (or fraction of a year). |
| Number of compounding periods per year | (n) | e.g., 12 for monthly, 4 for quarterly. |
Simple Interest
[ \boxed{SI = P \times r \times t} ]
Compound Interest – Amount (A)
[ \boxed{A = P \bigl(1 + \tfrac{r}{n}\bigr)^{n t}} ]
Compound Interest – Interest Earned
[ \boxed{CI = A - P = P \bigl(1 + \tfrac{r}{n}\bigr)^{n t} - P} ]
When the Compounding Period is Not an Integer
If (t) is not a whole number, use the same formula with (t) as a decimal (e.g., (t = 3.5) years).
3. Worked Example
Problem
A student deposits ₹12 000 in a bank at an annual interest rate of 8 % compounded quarterly.
Find:
- The amount after 5 years.
- The interest earned in those 5 years.
Solution
| Step | Calculation | Result |
|---|---|---|
| 1. Convert rate to decimal | (r = 8% = 0.08) | 0.08 |
| 2. Determine (n) | Quarterly → (n = 4) | 4 |
| 3. Plug into CI formula | (A = 12000 \left(1 + \frac{0.08}{4}\right)^{4 \times 5}) | |
| 4. Compute inside | (1 + \frac{0.08}{4} = 1 + 0.02 = 1.02) | |
| 5. Power | (4 \times 5 = 20) → (1.02^{20}) | |
| 6. Evaluate (1.02^{20}) | ≈ 1.485947 | |
| 7. Multiply by principal | (12000 \times 1.485947 ≈ ₹17 831.36) | ₹17 831.36 |
| 8. Interest earned | (CI = A - P = 17 831.36 - 12 000 ≈ ₹5 831.36) | ₹5 831.36 |
Answer
- Amount after 5 years ≈ ₹17 831.36
- Interest earned ≈ ₹5 831.36
4. Quick Revision Summary
| Topic | Key Take‑away |
|---|---|
| Simple Interest | (SI = P \times r \times t). No compounding, linear growth. |
| Compound Interest | (A = P(1 + r/n)^{nt}). Interest on interest → exponential growth. |
| Annual Rate to Decimal | Divide by 100. |
| Compounding Frequency | (n = 1) (annually), (2) (semi‑annually), (4) (quarterly), (12) (monthly), (365) (daily). |
| Non‑integer Time | Use decimal (t). Formula works the same. |
| Solving for Unknowns | Rearrange formulas: e.g., (t = \frac{\ln(A/P)}{n \ln(1 + r/n)}) for time. |
| Common Mistakes | 1) Forget to convert rate to decimal. 2) Use wrong (n). 3) Apply simple interest formula to a compound problem. |
| Practical Tip | For quick mental calculation, approximate compound growth by (A ≈ P(1 + rt)) if (r) is small and (t) short. |
Quick Practice Question (Try before checking the answer)
A sum of ₹5 000 is invested at 6 % per annum compounded half‑annually.
Find the amount after 3 years.
(Answer: ₹6 325.12)
End of Notes
Use these notes to review the core concepts, practice with similar problems, and stay sharp for the Karnataka Forest Guard exam.