Simple & Compound Interest – Study Notes
Program: Jharkhand Forest Guard
Subject: Quantitative Aptitude
Topic: Simple & Compound Interest
1. Simple Explanation
| Term | What It Means |
|---|---|
| Principal (P) | Initial amount of money borrowed or invested. |
| Rate of Interest (R) | Annual percentage rate at which interest is calculated. |
| Time (T) | Duration (in years) for which money is borrowed or invested. |
| Simple Interest (SI) | Interest calculated only on the principal. |
| Compound Interest (CI) | Interest calculated on the principal and on the interest that has accumulated over previous periods. |
- Simple Interest grows linearly with time.
- Compound Interest grows exponentially (faster than simple interest) because it “reinvests” the interest.
2. Key Points / Formulae
| Concept | Formula | Notes |
|---|---|---|
| Simple Interest | ( \text{SI} = \frac{P \times R \times T}{100} ) | Rate (R) is in percent, Time (T) in years. |
| Total Amount (A) | ( A = P + \text{SI} = P\left(1 + \frac{R T}{100}\right) ) | For cash flow calculations. |
| Compound Interest (Annual compounding) | ( A = P\left(1 + \frac{R}{100}\right)^{T} ) | Use integer (T) for whole years. |
| Compound Interest (n times per year) | ( A = P\left(1 + \frac{R}{100 n}\right)^{nT} ) | (n) = number of compounding periods per year. |
| Effective Annual Rate (EAR) | ( \text{EAR} = \left(1 + \frac{R}{100 n}\right)^{n} - 1 ) | Useful when comparing different compounding frequencies. |
| Finding Principal or Rate | Rearrange the appropriate formula. | e.g., ( P = \frac{A}{(1 + \frac{R}{100})^{T}} ) |
| Time in months | Convert months to years: ( T_{\text{yr}} = \frac{\text{months}}{12} ) | Keep consistent units. |
| Percentage to Decimal | ( \frac{R}{100} ) | Always convert before plugging into formulas. |
3. Worked Example
Problem
An investment of ₹12,000 is made at an annual simple interest rate of 4% for 3 years.
- Calculate the simple interest earned.
- Compute the total amount at the end of 3 years.
- Repeat the calculation for compound interest compounded annually at the same rate.
Solution
| Step | Calculation | Result |
|---|---|---|
| 1. Simple Interest | ( \text{SI} = \frac{12,000 \times 4 \times 3}{100} ) | ( \text{SI} = 1,440 ) |
| 2. Total Amount (SI) | ( A = 12,000 + 1,440 ) | ( A = 13,440 ) |
| 3. Compound Interest (annual) | ( A = 12,000 \left(1 + \frac{4}{100}\right)^{3} ) | ( A = 12,000 \times 1.04^{3} = 12,000 \times 1.124864 = 13,498.37 ) |
| 4. Compound Interest earned | ( \text{CI} = 13,498.37 - 12,000 ) | ( \text{CI} ≈ 1,498.37 ) |
Result Summary
| Interest Type | Interest Earned | Total Amount |
|---|---|---|
| Simple | ₹1,440 | ₹13,440 |
| Compound | ₹1,498.37 | ₹13,498.37 |
Observation: Compound interest gives a slightly higher return because interest on interest is added each year.
4. Quick Revision Summary
-
Simple Interest
- Formula: ( \text{SI} = \frac{PRT}{100} )
- Total: ( A = P + \text{SI} = P\left(1 + \frac{RT}{100}\right) )
- Linear growth.
-
Compound Interest
- Annual compounding: ( A = P\left(1 + \frac{R}{100}\right)^{T} )
- n‑times per year: ( A = P\left(1 + \frac{R}{100n}\right)^{nT} )
- Exponential growth; faster accumulation.
-
Key Conversion Tips
- Convert percentages to decimals before calculation.
- Convert months to years: divide by 12.
- Keep the same units for all variables.
-
Common Pitfalls
- Forgetting to divide the rate by 100.
- Mixing up years and months.
- Using the wrong compounding frequency.
-
Practice Tips
- Work out both simple and compound interest for the same principal, rate, and time to see the difference.
- Try varying ( n ) (e.g., monthly, quarterly) to understand its impact.
- Use the effective annual rate to compare different compounding schedules.
End of Notes