Lesson 1.6: Simple & Compound Interest

Introduction:
Interest problems are common in SSC exams, especially in CGL and CHSL arithmetic sections. Understanding the difference between Simple Interest (SI) and Compound Interest (CI) and knowing the formulas is crucial for quick calculations.

1. Simple Interest (SI)

• Definition: Interest calculated only on the principal amount.

• Formula:

SI=P×R×T100SI = \frac{P \times R \times T}{100}SI=100P×R×T​

Where:

• P = Principal

• R = Rate of Interest (% per annum)

• T = Time (in years)

• Example:
  P = ₹10,000, R = 5%, T = 2 years

SI=10000×5×2100=₹1000SI = \frac{10000 \times 5 \times 2}{100} = ₹1000SI=10010000×5×2​=₹1000

• Total Amount (A):

$$A=P+SI$$

Example: 10,000 + 1,000 = ₹11,000

2. Compound Interest (CI)

• Definition: Interest calculated on Principal + Previous Interest for each period.

• Formula (Annually Compounded):

A=P(1+R100)TA = P \left(1 + \frac{R}{100}\right)^TA=P(1+100R​)T $$CI=A-P$$

• Example:
  P = ₹10,000, R = 10%, T = 2 years

A=10000(1+10100)2=10000×1.12=12100A = 10000 \left(1 + \frac{10}{100}\right)^2 = 10000 \times 1.1^2 = 12100A=10000(1+10010​)2=10000×1.12=12100 $$CI=12100-10000=₹2100$$

• Shortcut for 2 years:

CI≈SI+SI×R100CI \approx SI + \frac{SI \times R}{100}CI≈SI+100SI×R​

This works well for small R%.

3. Key SSC Tricks

• For half-yearly/quarterly/monthly compounding, adjust R and T accordingly:

  Reffective=Rn,Teffective=n×yearsR_{\text{effective}} = \frac{R}{n}, \quad T_{\text{effective}} = n \times \text{years} Reffective​=nR​,Teffective​=n×years

  where n = number of compounding periods per year.

• Remember: CI > SI if R > 0 and T > 1 year.

4. Practice Questions

1. Find SI on ₹8,000 at 6% per annum for 3 years.

2. Find CI on ₹5,000 at 10% per annum for 2 years (compounded annually).

3. A sum of ₹12,000 amounts to ₹13,320 in 2 years at simple interest. Find the rate of interest.

4. P = ₹10,000, R = 8% compounded annually. Find CI for 3 years.

5. A sum of ₹15,000 is invested at 5% per annum CI. Find total amount after 2 years if compounded half-yearly.