Punjab TET – Quantitative Aptitude
Simple & Compound Interest
Goal: Understand the concepts, learn the formulas, and master quick calculations to score confidently in the exam.
1. Simple Explanation
| Concept | What it is | How it works |
|---|---|---|
| Simple Interest (SI) | Interest earned only on the original amount (principal). | SI = P × R × T (P = principal, R = annual rate, T = time in years). |
| Compound Interest (CI) | Interest earned on the original amount and on the accumulated interest from previous periods. | CI = P × [(1 + R/n)^(nT) – 1] (n = compounding periods per year). |
Key difference:
- SI is linear in time.
- CI grows exponentially; the longer the money is invested and the more frequent the compounding, the higher the yield.
2. Key Points to Remember
| Item | Detail |
|---|---|
| Principal (P) | Initial amount of money. |
| Rate (R) | Annual interest rate (expressed as a percentage, e.g., 8 % → 0.08). |
| Time (T) | Duration of investment/loan in years. |
| Compounding Frequency (n) | How many times interest is compounded per year (1 = yearly, 2 = half‑yearly, 4 = quarterly, 12 = monthly, 365 = daily). |
| Formula for Simple Interest | SI = P × R × T |
| Formula for Compound Interest | CI = P × [(1 + R/n)^(nT) – 1] |
| Total Amount (A) | A = P + SI for SI; A = P + CI for CI. |
| Effect of Compounding | More compounding periods → higher CI for the same R and T. |
| Conversion of Rate & Time | If R is given per month, convert to annual: R_ann = R_month × 12. If T is in months, convert to years: T_years = T_month ÷ 12. |
| Common Pitfalls | 1. Forgetting to divide rate by 100. 2. Mixing up time units. 3. Using wrong n for CI. 4. Ignoring that CI formula already includes the principal. |
3. Worked Example
Problem
A student deposits ₹10,000 in a bank that offers 12 % per annum simple interest.
a) What will be the simple interest after 3 years?
b) If the bank offers 8 % per annum compounded quarterly, what will be the amount after 3 years?
a) Simple Interest
Step 1 – Identify variables
- P = ₹10,000
- R = 12 % = 0.12
- T = 3 years
Step 2 – Apply formula
SI = P × R × T
SI = 10,000 × 0.12 × 3
SI = 10,000 × 0.36
SI = ₹3,600
Step 3 – Total amount
A = P + SI = 10,000 + 3,600 = ₹13,600
b) Compound Interest (Quarterly)
Step 1 – Identify variables
- P = ₹10,000
- R = 8 % = 0.08
- T = 3 years
- n = 4 (quarterly)
Step 2 – Apply CI formula
CI = P × [(1 + R/n)^(nT) – 1]
= 10,000 × [(1 + 0.08/4)^(4×3) – 1]
= 10,000 × [(1 + 0.02)^12 – 1]
= 10,000 × [1.02^12 – 1]
Compute 1.02^12 (use calculator or approximation):
1.02^12 ≈ 1.26824
CI ≈ 10,000 × (1.26824 – 1)
CI ≈ 10,000 × 0.26824
CI ≈ ₹2,682.40
Step 3 – Total amount
A = P + CI = 10,000 + 2,682.40 = ₹12,682.40
Quick Recap of the Calculations
| Type | Formula | Result |
|---|---|---|
| SI | SI = P × R × T |
₹3,600 |
| CI (quarterly) | CI = P × [(1 + R/n)^(nT) – 1] |
₹2,682.40 |
| Total (SI) | A = P + SI |
₹13,600 |
| Total (CI) | A = P + CI |
₹12,682.40 |
4. Quick Revision Summary
- SI grows linearly:
SI = PRT. - CI grows exponentially:
CI = P[(1 + R/n)^(nT) – 1]. - Compound frequency (n): 1 = yearly, 2 = half‑yearly, 4 = quarterly, 12 = monthly, 365 = daily.
- To compare: keep R and T same, vary n to see the effect.
- Always check units (rate as decimal