Simple Interest
Overview
Simple Interest (SI) is one of the most straightforward yet frequently tested topics in OTET Paper I Mathematics. It forms the foundation of commercial mathematics and helps students understand how money grows over time when borrowed or invested. This concept directly connects classroom learning to real-life situations like bank deposits, loans, and installment purchases.
For OTET, you must master the basic formula, understand what each variable represents, and solve word problems quickly. Questions typically involve finding any one of the four quantities (SI, Principal, Rate, or Time) when the other three are given. The topic also appears in combination with problems involving Amount, which adds Principal and Interest together.
Since this is tested at the primary level (Classes I-V context), the numerical calculations remain simple, but conceptual clarity is essential for both solving problems and teaching young learners effectively.
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Key Concepts
- **Principal (P):** The original sum of money borrowed or invested, before any interest is added. This is the starting amount.
- **Rate of Interest (R):** The percentage charged or earned per year (per annum). Always expressed as "percent per annum" unless stated otherwise.
- **Time (T):** The duration for which money is borrowed or invested. Usually given in years; if given in months, convert to years by dividing by 12.
- **Simple Interest (SI):** The extra money paid or earned on the principal. In simple interest, this is calculated only on the original principal, not on accumulated interest.
- **Amount (A):** The total money after adding interest to the principal. Amount = Principal + Simple Interest.
- **"Per Annum" means "per year":** When rate is 5% per annum, it means 5% of principal is charged as interest each year.
- **Interest remains constant each year:** Unlike compound interest, simple interest gives the same interest amount every year because it is always calculated on the original principal.
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Formulas / Key Facts
**Primary Formula:** SI = (P × R × T) / 100
Where:
- SI = Simple Interest
- P = Principal (in rupees)
- R = Rate of interest (percent per annum)
- T = Time (in years)
**Derived Formulas:**
- P = (SI × 100) / (R × T) — To find Principal
- R = (SI × 100) / (P × T) — To find Rate
- T = (SI × 100) / (P × R) — To find Time
**Amount Formula:** A = P + SI or A = P + (P × R × T) / 100 or A = P(1 + RT/100)
**Time Conversion:**
- If time is in months: T = Number of months / 12
- If time is in days: T = Number of days / 365
**Key Fact:** When P, R, and T are doubled, SI becomes 8 times (since SI is directly proportional to each).
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Worked Examples
**Example 1: Finding Simple Interest**
*Problem:* Find the simple interest on Rs 5000 at 8% per annum for 3 years.
*Solution:*
- P = 5000, R = 8, T = 3
- SI = (P × R × T) / 100
- SI = (5000 × 8 × 3) / 100
- SI = 120000 / 100
- SI = Rs 1200
**Answer:** Simple Interest = Rs 1200
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**Example 2: Finding Principal**
*Problem:* The simple interest on a certain sum for 4 years at 5% per annum is Rs 800. Find the principal.
*Solution:*
- SI = 800, R = 5, T = 4
- P = (SI × 100) / (R × T)
- P = (800 × 100) / (5 × 4)
- P = 80000 / 20
- P = Rs 4000
**Answer:** Principal = Rs 4000
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**Example 3: Finding Time (with Amount given)**
*Problem:* At what time will Rs 1500 amount to Rs 1800 at 4% per annum simple interest?
*Solution:*
- First find SI: SI = Amount − Principal = 1800 − 1500 = Rs 300
- P = 1500, R = 4, SI = 300
- T = (SI × 100) / (P × R)
- T = (300 × 100) / (1500 × 4)
- T = 30000 / 6000
- T = 5 years
**Answer:** Time = 5 years
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**Example 4: Time in Months**
*Problem:* Find SI on Rs 2400 at 10% per annum for 9 months.
*Solution:*
- Convert months to years: T = 9/12 = 3/4 years = 0.75 years
- SI = (P × R × T) / 100
- SI = (2400 × 10 × 0.75) / 100
- SI = 18000 / 100
- SI = Rs 180
**Answer:** Simple Interest = Rs 180
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Common Mistakes
- **Forgetting to convert months to years:** Students directly use 6 months as T = 6 instead of T = 6/12 = 0.5. → **Fix:** Always express time in years before substituting in the formula.
- **Confusing Amount with Simple Interest:** Some students calculate SI but write it as the final answer when Amount is asked. → **Fix:** Read the question carefully. If Amount is asked, add SI to Principal.
- **Using Rate as a decimal without adjusting the formula:** Writing R = 0.05 instead of 5, then still dividing by 100. → **Fix:** In the standard formula, use R as a whole number (5, not 0.05) since division by 100 is already in the formula.
- **Mixing up what to find:** In word problems, students sometimes solve for the wrong variable. → **Fix:** First identify what is given and what is asked. Write down P, R, T, SI, A clearly before starting.
- **Calculation errors in division:** When finding P or T, the division involves multiple numbers and students often make arithmetic errors. → **Fix:** Simplify step by step; cancel common factors before final division.
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Quick Reference
- **SI = (P × R × T) / 100** — The master formula; memorize this first.
- **Amount = Principal + Simple Interest** — Always add, never subtract.
- **Time in months? Divide by 12** — Convert to years before using formula.
- **SI is directly proportional to P, R, and T** — Double any one, SI doubles.
- **To find P, R, or T:** Cross-multiply and rearrange the SI formula.
- **Check units:** Rate should be in percent per annum; time in years.