Simple Interest — Study Notes for Bihar TET Paper I

Overview

Simple Interest (SI) is a foundational topic in commercial mathematics that appears consistently in Bihar TET Paper I. It tests your ability to calculate the extra money earned or paid on a principal amount over time at a fixed rate. This topic directly connects to real-life situations like bank deposits, loans, and instalments — making it essential for primary-level teaching.

For Bihar TET, you need to master the basic formula, understand the relationship between principal, rate, time, and interest, and solve word problems quickly. Questions typically involve finding any one of the four variables (SI, P, R, or T) when three are given, or comparing different investment scenarios. The calculations are straightforward but require careful attention to units — especially converting months to years.

This topic also links to percentage calculations and ratio-proportion, so a strong grasp here strengthens your overall quantitative ability. Expect 1–2 direct questions on SI in the mathematics section.

Key Concepts

• **Principal (P)**: The original sum of money borrowed or invested. This is your starting amount before any interest is added.

• **Rate of Interest (R)**: The percentage charged or earned per year (per annum). Always expressed as "% per annum" unless stated otherwise.

• **Time (T)**: The duration for which money is borrowed or invested. Must be converted to years for the standard formula.

• **Simple Interest (SI)**: The extra money paid or earned, calculated only on the original principal — not on accumulated interest.

• **Amount (A)**: The total money at the end of the time period. Amount = Principal + Simple Interest.

• **Interest is directly proportional**: If you double the principal, rate, or time (keeping others constant), the SI also doubles. This proportionality is key to solving comparison problems.

• **SI does not compound**: Unlike compound interest, SI is calculated on the original principal throughout — the interest earned does not earn further interest.

Formulas / Key Facts

**Primary Formula:** SI = (P × R × T) / 100

Where P = Principal, R = Rate per annum (%), T = Time in years

**To find Principal:** P = (SI × 100) / (R × T)

**To find Rate:** R = (SI × 100) / (P × T)

**To find Time:** T = (SI × 100) / (P × R)

**Amount Formula:** A = P + SI A = P + (P × R × T) / 100 A = P(1 + RT/100)

**Time Conversion:**

• Months to years: Divide by 12 (e.g., 6 months = 6/12 = 0.5 years)
• Days to years: Divide by 365 (e.g., 73 days = 73/365 = 1/5 years)

**Useful Fact:** If SI equals Principal, then R × T = 100

Worked Examples

**Example 1: Finding Simple Interest** Find the simple interest on ₹5,000 at 8% per annum for 3 years.

Solution:

• P = ₹5,000, R = 8%, T = 3 years
• SI = (P × R × T) / 100
• SI = (5000 × 8 × 3) / 100
• SI = 120000 / 100
• SI = ₹1,200

**Example 2: Finding Principal** A sum of money at 10% per annum amounts to ₹7,700 in 2 years. Find the principal.

Solution:

• A = ₹7,700, R = 10%, T = 2 years
• We know A = P + SI = P + (P × R × T)/100
• 7700 = P + (P × 10 × 2)/100
• 7700 = P + P/5
• 7700 = 6P/5
• P = 7700 × 5/6
• P = ₹6,416.67 (approximately)

Alternative method:

• SI for ₹100 in 2 years at 10% = ₹20
• Amount for ₹100 = ₹120
• If ₹120 corresponds to ₹7,700
• Then P = (7700 × 100)/120 = ₹6,416.67

**Example 3: Time in Months** Find SI on ₹4,800 at 5% per annum for 9 months.

Solution:

• P = ₹4,800, R = 5%, T = 9/12 = 3/4 years
• SI = (4800 × 5 × 3/4) / 100
• SI = (4800 × 5 × 3) / (100 × 4)
• SI = 72000 / 400
• SI = ₹180

Common Mistakes

• **Forgetting to convert months to years** → Always divide months by 12 before applying the formula. If time is given as "18 months," use T = 18/12 = 1.5 years, not 18.

• **Confusing Amount with Simple Interest** → Amount is the total (P + SI), not just the interest. When a question asks "what amount will he receive," add SI to principal.

• **Using Rate as a decimal incorrectly** → In the formula SI = PRT/100, use R as a whole number (like 8 for 8%). Don't write 0.08 and then also divide by 100.

• **Misreading "per annum"** → Rate is always per year unless specified. If the question says "6% for 2 years," don't multiply 6 by 2 for the rate — only time changes.

• **Calculation errors with fractions** → When time is 2 years 6 months, write it as 2.5 years or 5/2 years. Students often add 2 + 6 = 8 incorrectly.

Quick Reference

• SI = (P × R × T) / 100 — the master formula for all SI problems

• Amount = Principal + Simple Interest

• Convert months to years: divide by 12

• SI doubles when P, R, or T doubles (direct proportion)

• If SI = P, then R × T = 100

• For quick calculation: Find SI on ₹100 first, then scale to actual principal