Karnataka TET – Quantitative Aptitude
Simple & Compound Interest
Goal: Master the concepts, formulas, and quick‑solve techniques needed for the TET exam.
1. Simple Explanation
| Concept | What it is | When it is used |
|---|---|---|
| Interest | The extra amount earned or paid on a principal. | All loan/savings problems |
| Simple Interest (SI) | Interest calculated only on the original principal. | Fixed‑rate loans, short‑term investments |
| Compound Interest (CI) | Interest earned on the principal and on previously earned interest. | Savings accounts, long‑term loans, investments |
Key Idea: In SI the interest never “re‑matures”; in CI the interest itself earns interest.
2. Key Formulas
| Variable | Symbol | Formula | Notes |
|---|---|---|---|
| Principal | (P) | – | Initial amount |
| Rate | (R) | – | Annual rate in % |
| Time | (T) | – | In years (fractional if needed) |
| Simple Interest | (SI) | (\displaystyle SI = \frac{P \times R \times T}{100}) | |
| Amount (Simple) | (A_{SI}) | (A_{SI} = P + SI) | |
| Compound Interest | (CI) | (\displaystyle CI = P\left[\left(1+\frac{r}{n}\right)^{nT}-1\right]) | (r = R/100) |
| Amount (Compound) | (A_{CI}) | (A_{CI} = P\left(1+\frac{r}{n}\right)^{nT}) | |
| Annual compounding | (n=1) | (A_{CI}=P(1+r)^T) | |
| Monthly compounding | (n=12) | (A_{CI}=P\left(1+\frac{r}{12}\right)^{12T}) | |
| Continuous compounding |