Simple Interest — CG TET Paper I Mathematics
Overview
Simple Interest (SI) is one of the most straightforward yet frequently tested topics in CG TET Paper I Mathematics. It forms the foundation of commercial mathematics and helps students understand how money grows over time when lent or borrowed. At the primary level, this topic connects mathematics to real-life situations — savings accounts, loans, and everyday financial transactions.
For CG TET, you must master the basic formula, understand each variable clearly, and solve problems quickly. Questions typically involve direct application of the formula or finding one unknown when other values are given. The topic also links to percentage calculations and ratio-proportion, so a strong grasp here strengthens your overall quantitative ability.
Speed and accuracy matter — most problems can be solved in under a minute if you know the formula variations well.
Key Concepts
- Principal (P): The original sum of money borrowed or invested before any interest is added. This is your starting amount.
- 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. Convert months to years (divide by 12) and days to years (divide by 365) when needed.
- Simple Interest (SI): Interest calculated only on the original principal throughout the entire period. Unlike compound interest, it does not include "interest on interest."
- Amount (A): The total money returned or accumulated after the time period. Amount = Principal + Simple Interest.
- Relationship between variables: All four quantities (P, R, T, SI) are directly proportional when others are constant — double the time, double the interest.
- Annual vs other periods: If rate is given per annum but time is in months, always convert time to years before applying the formula.
Formulas / Key Facts
Primary Formula: SI = (P × R × T) / 100
Amount Formula: A = P + SI = P + (P × R × T) / 100 = P(1 + RT/100)
Finding Principal: P = (SI × 100) / (R × T)
Finding Rate: R = (SI × 100) / (P × T)
Finding Time: T = (SI × 100) / (P × R)
Finding Principal from Amount: P = (A × 100) / (100 + RT)
Key Fact 1: When SI equals the Principal, then R × T = 100.
Key Fact 2: Money doubles at SI when R × T = 100 (e.g., 10% for 10 years, 20% for 5 years).
Key Fact 3: Money triples when R × T = 200; quadruples when R × T = 300.
Key Fact 4: If time is given in months, use T = months/12 in the formula.
Worked Examples
Example 1: Basic SI Calculation
Find the Simple Interest on Rs 5000 at 8% per annum for 3 years.
Step 1: Identify values — P = 5000, R = 8, T = 3
Step 2: Apply formula — SI = (P × R × T) / 100
Step 3: Calculate — SI = (5000 × 8 × 3) / 100 = 120000 / 100 = Rs 1200
Answer: Rs 1200
Example 2: Finding Time
At what time will Rs 2000 amount to Rs 2300 at 5% per annum simple interest?
Step 1: Find SI — SI = Amount - Principal = 2300 - 2000 = Rs 300
Step 2: Use formula — T = (SI × 100) / (P × R)
Step 3: Calculate — T = (300 × 100) / (2000 × 5) = 30000 / 10000 = 3 years
Answer: 3 years
Example 3: Finding Rate
A sum of Rs 4000 becomes Rs 5200 in 4 years at simple interest. Find the rate of interest.
Step 1: Find SI — SI = 5200 - 4000 = Rs 1200
Step 2: Use formula — R = (SI × 100) / (P × T)
Step 3: Calculate — R = (1200 × 100) / (4000 × 4) = 120000 / 16000 = 7.5%
Answer: 7.5% per annum
Example 4: Time in Months
Find SI on Rs 3600 at 10% per annum for 9 months.
Step 1: Convert time — T = 9/12 = 3/4 years = 0.75 years
Step 2: Apply formula — SI = (3600 × 10 × 0.75) / 100 = 27000 / 100 = Rs 270
Answer: Rs 270
Common Mistakes
- Forgetting to convert months to years → Always check the unit of time. If R is per annum and T is in months, divide months by 12 before calculating.
- Confusing Amount with Simple Interest → Students sometimes use Amount in place of SI in the formula. Remember: SI is only the interest earned, not the total sum.
- Calculating percentage incorrectly → Some students forget to divide by 100. The formula has division by 100 built in because R is in percentage form.
- Mixing up SI and Compound Interest logic → In SI, interest remains constant each year. Do not add previous year's interest to principal for the next calculation.
- Using wrong formula rearrangement → When finding P, R, or T, ensure you rearrange correctly. Cross-multiply carefully: if SI = PRT/100, then P = 100×SI / (R×T).
Quick Reference
- SI = (P × R × T) / 100 — memorize this first.
- Amount = Principal + SI.
- Money doubles when R × T = 100.
- Always convert months to years: T(years) = months ÷ 12.
- To find any unknown, rearrange: Unknown = (SI × 100) / (product of other two).
- SI remains same each year; total SI = yearly SI × number of years.