📚 Simple & Compound Interest – Quick Study Notes
(For Rajasthan Patwari / Lekhpal Quantitative Aptitude)
1️⃣ Simple Explanation
| Concept | What it means | When it’s used |
|---|---|---|
| Simple Interest (SI) | Interest earned only on the initial principal for the entire period | Short‑term loans, savings accounts with yearly rates, fixed‑term deposits, etc. |
| Compound Interest (CI) | Interest earned on the initial principal and on all previously accrued interest | Long‑term investments, loans with periodic compounding (monthly, quarterly, etc.) |
Key idea:
- Simple = one‑time calculation of interest.
- Compound = interest keeps “compounding” – it’s added to the principal and then earns interest again.
2️⃣ Key Points & Formulas
| Metric | Formula | Notes |
|---|---|---|
| Simple Interest | (\displaystyle SI = \frac{P \times R \times T}{100}) | P = principal, R = annual rate (%), T = time in years. |
| Amount (A) after SI | (\displaystyle A = P + SI = P\left(1 + \frac{R \times T}{100}\right)) | |
| Compound Interest | (\displaystyle CI = P\left(\left(1 + \frac{R}{n \times 100}\right)^{nT} - 1\right)) | n = compounding frequency per year (12 for monthly, 4 for quarterly, etc.) |
| Amount (A) after CI | (\displaystyle A = P\left(1 + \frac{R}{n \times 100}\right)^{nT}) | |
| Effective Annual Rate (EAR) | (\displaystyle EAR = \left(1 + \frac{R}{n}\right)^n - 1) | Useful to compare different compounding schedules. |
| Monthly/Quarterly Rate | (\displaystyle r = \frac{R}{n}) | Use when calculations are done in the compounding period. |
Common Pitfalls
- Time Units – Ensure T is in years. If given in months, convert: (T_{\text{yr}} = \frac{\text{months}}{12}).
- Rate Conversion – Convert rate to decimal when plugging into formulas: e.g., 8 % → 0.08.
- Compounding Frequency – Use the correct n. For “annually” (n = 1), “quarterly” (n = 4), “monthly” (n = 12).
- Rounding – Round only at the final answer unless the problem specifies intermediate rounding.
3️⃣ Worked Example
📌 Problem
A Patwari deposits ₹10,000 in a bank at an annual interest rate of 6 %.
- Part A: How much will he have after 3 years if the interest is simple?
- Part B: How much will he have after 3 years if the interest is compounded quarterly?
- Part C: What is the difference between the two amounts?
3.1 Simple Interest Calculation
-
Identify variables
- (P = ₹10,000)
- (R = 6%)
- (T = 3) years
-
Compute SI
[ SI = \frac{10,000 \times 6 \times 3}{100}=₹1,800 ] -
Total amount
[ A_{\text{SI}} = P + SI = 10,000 + 1,800 = ₹11,800 ]
3.2 Compound Interest Calculation (Quarterly)
-
Convert variables
- Annual rate (R = 6%) → quarterly rate (r = \frac{6}{4} = 1.5%)
- Compounding frequency (n = 4)
- Time (T = 3) years
-
Formula
[ A_{\text{CI}} = 10,000 \left(1 + \frac{6}{4 \times 100}\right)^{4 \times 3} = 10,000 \left(1 + 0.015\right)^{12} ] -
Compute
[ 1.015^{12} \approx 1.195618 ] [ A_{\text{CI}} \approx 10,000 \times 1.195618 = ₹11,956.18 ] -
CI amount
[ CI \approx ₹11,956.18 - ₹10,000 = ₹1,956.18 ]
3.3 Difference
[ \text{Difference} = A_{\text{CI}} - A_{\text{SI}} = 11,956.18 - 11,800 = ₹156.18 ]
Answer:
- Simple interest amount after 3 years: ₹11,800
- Compound interest amount (quarterly) after 3 years: ₹11,956.18
- The compounded amount is ₹156.18 higher.
4️⃣ Quick Revision Summary
| Topic | Key Formula | Quick Tip |
|---|---|---|
| Simple Interest | (SI = \frac{PRT}{100}) | Multiply P by R × T and divide by 100. |
| Amount (SI) | (A = P + SI) | Plug in P and SI directly. |
| Compound Interest | (CI = P\left(\left(1 + \frac{R}{n \times 100}\right)^{nT} - 1\right)) | First find the quarterly/monthly rate, raise to the power of total periods, subtract 1, multiply by P. |
| ** |