Haryana PSC – Quantitative Aptitude
Simple & Compound Interest – Complete Study Notes
These notes are written in a clear, step‑by‑step style suitable for quick revision before the exam.
All formulas are kept in the most compact form so you can memorize them easily.
1. Simple Interest (SI)
1.1 What is it?
Simple Interest is the interest earned only on the original principal for each period.
1.2 Formula
[ \boxed{\text{SI} = \frac{P \times R \times T}{100}} ]
- P = Principal (initial amount)
- R = Annual rate of interest (in %)
- T = Time (in years)
Total Amount (A) after (T) years
[ \boxed{A = P + \text{SI} = P \left(1 + \frac{R,T}{100}\right)} ]
1.3 Quick Calculation Steps
- Compute ( \frac{R \times T}{100} ) (this is the interest factor).
- Multiply the factor by P to get SI.
- Add SI to P for the total amount.
1.4 Typical PSC Questions
- Find the amount after n years at r% simple interest.
- Find the rate if the amount and time are given.
- Find the principal if the amount, rate, and time are known.
2. Compound Interest (CI)
2.1 What is it?
Compound Interest is interest earned on the original principal and on the interest accumulated in previous periods.
2.2 Formula
[ \boxed{A = P\left(1 + \frac{R}{n}\right)^{nT}} ]
- P = Principal
- R = Annual rate of interest (in %)
- n = Number of compounding periods per year
- T = Time (in years)
The Compound Interest itself: [ \boxed{\text{CI} = A - P} ]
Effective Annual Rate (EAR) (if compounding is more than once a year): [ \boxed{\text{EAR} = \left(1 + \frac{R}{n}\right)^{n} - 1} ]
2.3 Common Compounding Frequencies
| Frequency | n | Example |
|---|---|---|
| Yearly | 1 | (A = P(1 + R/100)) |
| Half‑Yearly | 2 | (A = P\left(1 + \frac{R}{2}\right)^2) |
| Quarterly | 4 | (A = P\left(1 + \frac{R}{4}\right)^4) |
| Monthly | 12 | (A = P\left(1 + \frac{R}{12}\right)^{12}) |
| Daily | 365 | (A = P\left(1 + \frac{R}{365}\right)^{365}) |
2.4 Quick Calculation Steps
- Convert R to decimal: (r = R/100).
- Compute the base: (1 + r/n).
- Raise to the power (nT).
- Multiply by P to get A.
- Subtract P to get CI.
2.5 Typical PSC Questions
- Find the amount after t years with n compounding periods at r%.
- Find the rate if the amount, principal, and compounding frequency are known.
- Compare simple vs. compound interest over a period.
3. Worked Example – Simple & Compound
3.1 Problem Statement
A person invests ₹50,000 for 4 years.
(i) If the simple interest rate is 6% per annum, what is the total amount?
(ii) If the same amount is invested at 6% per annum compounded quarterly, what is the total amount?
3.2 Solution
| Part | Step | Calculation | Result |
|---|---|---|---|
| (i) Simple Interest | 1. Compute SI factor | (\frac{R \times T}{100} = \frac{6 \times 4}{100} = 0.24) | |
| 2. SI | (P \times 0.24 = 50,000 \times 0.24 = 12,000) | ||
| 3. Total Amount | (P + \text{SI} = 50,000 + 12,000 = 62,000) | ₹62,000 | |
| (ii) Compound Interest (Quarterly) | 1. Convert R | (r = 6/100 = 0.06) | |
| 2. Base | (1 + r/n = |