Maharashtra Police Constable – Quantitative Aptitude
Topic: Simple & Compound Interest
Study Notes – concise, clear, and exam‑ready.
Format: Markdown, with a simple explanation, key points, worked example(s), and a quick revision summary.
1. Simple Interest (SI)
1.1 What is it?
Simple Interest is the interest calculated only on the initial principal for the entire period.
1.2 Formula
[ \text{SI} = \frac{P \times R \times T}{100} ]
- P – Principal (initial amount)
- R – Annual rate of interest (in %)
- T – Time (in years)
1.3 Amount after T years
[ A = P + \text{SI} = P\left(1 + \frac{R \times T}{100}\right) ]
2. Compound Interest (CI)
2.1 What is it?
Compound Interest is the interest calculated on the initial principal plus all accumulated interest over time. The amount “compounds” at a specified frequency.
2.2 Formula
[ A = P\left(1 + \frac{R}{n}\right)^{nT} ]
- n – Number of compounding periods per year
- T – Time (years)
- R – Annual rate of interest (in %)
Compound Interest earned
[
\text{CI} = A - P
]
2.3 Common Compounding Frequencies
| In words | n | Example |
|---|---|---|
| Annually | 1 | yearly compounding |
| Semi‑annually | 2 | twice a year |
| Quarterly | 4 | four times a year |
| Monthly | 12 | every month |
| Daily | 365 | every day |
3. Key Points for the Exam
| Topic | Key Point | Quick Tip |
|---|---|---|
| SI | Use directly when period is short or interest is not compounded | “SI” → “simple” → no compounding |
| CI | Must identify compounding frequency (n) | Write n first, then use formula |
| Conversion | Convert rate to decimal: (R% = \frac{R}{100}) | R/100 before dividing by n |
| Exponents | (nT) = total number of compounding periods | Multiply T by n, not the reverse |
| Rounding | Use calculator for precision; round only at the end | “Rounding at the end” avoids compounding errors |
| Common Mistake | Forgetting to use the same units for time | Ensure T is in years |
| Approximation | For small rates, (1+r)^n ≈ 1 + nr | Useful for quick sanity checks |
4. Worked Example
Problem
A person deposits ₹15,000 in a bank at an annual interest rate of 6 % compounded quarterly for 3 years. Find the amount and the compound interest earned.
Step‑by‑Step
| Step | Calculation | Result |
|---|---|---|
| 1 | Convert rate to decimal: (R = 6% = 0.06) | 0.06 |
| 2 | Determine n (quarterly compounding): (n = 4) | 4 |
| 3 | Compute (nT = 4 \times 3 = 12) | 12 |
| 4 | Compute (\frac{R}{n} = \frac{0.06}{4} = 0.015) | 0.015 |
| 5 | Apply CI formula: (A = 15000 \times (1 + 0.015)^{12}) | |
| 6 | ((1 + 0.015)^{12} ≈ 1.195618) | |
| 7 | (A = 15000 \times 1.195618 ≈ ₹17,934.27) | 17,934.27 |
| 8 | CI = A – P = 17,934.27 – 15,000 = ₹2,934.27 | 2,934.27 |
Answer
- Amount after 3 years: ₹17,934.27
- Compound Interest earned: ₹2,934.27
5. Quick Revision Summary (Bullet Points)
-
Simple Interest (SI)
- ( \text{SI} = \dfrac{P \times R \times T}{100} )
- ( A = P + \text{SI} )
-
Compound Interest (CI)
- ( A = P\left(1 + \dfrac{R}{n}\right)^{nT} )
- ( \text{CI} = A - P )
-
Steps to solve
- Convert rate to decimal.
- Identify compounding frequency (n).
- Compute total periods (nT).
- Plug into the