Simple & Compound Interest – SSC Stenographer Study Notes
Purpose – These notes are written to help you quickly review the key concepts, formulas, and steps required for the Simple & Compound Interest section of the SSC Stenographer exam.
1. Simple Interest (SI)
1.1. Simple Explanation
Simple interest is the cost of borrowing or the return on investment calculated only on the original amount (principal). The interest does not accumulate on previously earned interest.
1.2. Key Formula
[ \text{SI} = \frac{P \times R \times T}{100} ]
| Symbol | Meaning |
|---|---|
| (P) | Principal (initial amount) |
| (R) | Rate of interest per annum (in %) |
| (T) | Time period (in years) |
| (\text{SI}) | Simple interest earned |
1.3. Total Amount
[ \text{Total Amount} = P + \text{SI} ]
2. Compound Interest (CI)
2.1. Simple Explanation
Compound interest is the interest calculated on the original principal plus on all the interest that has already been earned. It “compounds” over the compounding periods.
2.2. Key Formula
[ \text{CI} = P \left( \left(1 + \frac{R}{n}\right)^{nT} \right) - P ]
| Symbol | Meaning |
|---|---|
| (P) | Principal |
| (R) | Rate of interest per annum (in %) |
| (T) | Time period (in years) |
| (n) | Number of compounding periods per year |
| (\text{CI}) | Compound interest earned |
2.3. Total Amount
[ \text{Total Amount} = P + \text{CI} = P \left(1 + \frac{R}{n}\right)^{nT} ]
2.4. Special Cases
| Compounding | Formula |
|---|---|
| Annual | (n = 1) |
| Semi‑annual | (n = 2) |
| Quarterly | (n = 4) |
| Monthly | (n = 12) |
| Daily (approx.) | (n = 365) |
| Continuous | (A = P,e^{RT/100}) (use when “continuous compounding” is mentioned) |
3. Quick Rules & Tips
| Rule | What it Helps |
|---|---|
| Rule of 72 | Approximate years to double at a given rate: (\text{Years} \approx 72 / R) |
| Rule of 115 | Approximate years to triple: (\text{Years} \approx 115 / R) |
| Deciding Between SI & CI | If the problem states “simple interest” → use SI formula. Otherwise, default to CI unless explicitly mentioned. |
| Finding Time (T) | Rearrange SI formula: (T = \frac{100 \times \text{SI}}{P \times R}). |
| Finding Rate (R) | SI: (R = \frac{100 \times \text{SI}}{P \times T}). CI: use logs or trial‑and‑error. |
| Finding Principal (P) | SI: (P = \frac{100 \times \text{SI}}{R \times T}). CI: (P = \frac{\text{Amount}}{(1 + R/n)^{nT}}). |
4. Worked Example
4.1. Problem Statement
Q: A person deposits ₹12,000 in a bank at an annual interest rate of 7 % compounded quarterly. What will be the total amount after 4 years?
4.2. Identify Known Values
- (P = ₹12{,}000)
- (R = 7%,\text{per annum})
- (n = 4) (quarterly)
- (T = 4) years
4.3. Plug into CI Formula
[ \begin{aligned} A &= P \left(1 + \frac{R}{n}\right)^{nT} \ &= 12{,}000 \left(1 + \frac{7}{4}\right)^{4 \times 4} \quad\text{(convert } R\text{ to decimal: } \frac{7}{100})\ &= 12{,}000 \left(1 + 0.0175\right)^{16} \ &= 12{,}000 \times (1.0175)^{16} \end{aligned} ]
4.4. Compute ((1.0175)^{16})
Using a calculator (or log tables):
[ (1.0175)^{16} \approx 1.3083 ]
4.5. Final Amount
[ A \approx 12{,}000 \times 1.3083 \approx ₹15{,}699.60 ]
Answer: After 4 years, the account will hold approximately ₹15,700.
5. Quick Revision Summary
- Simple Interest (SI)
[ \text{SI} = \frac{PRT}{100} \