Mathematics • Class 6 Appendix-II Item 11 150 Mins Overall

Simple Interest

Pointwise AISSEE Class 6 Mathematics guide for Simple Interest (Topic 11). Master PRT/100, deriving principal, rate, and time, converting days/months to years, and sum-doubling formulas.

Overview & Fundamental Concept

Pointwise AISSEE Class 6 Mathematics guide for Simple Interest (Topic 11). Master PRT/100, deriving principal, rate, and time, converting days/months to years, and sum-doubling formulas.

Official Syllabus Coverage Breakdown
Syllabus Item Prescribed Scope Exam Relevance & Pedagogical Objective
Item 11 Principal, rate of interest per annum, time period, simple interest formula, total amount payable. Master principal, rate, time parameter definitions, SI and Amount calculations, month/day year conversions, and sum-multiplying shortcuts for AISSEE Class VI.
1. Core Parameters: Principal, Rate, Time & Amount
  • Principal ($P$): The sum of money borrowed, lent, or deposited into an account upon which interest is charged.
  • Rate of Interest ($R$): The interest charged on ₹100 for a duration of one year, expressed as a percentage per annum ($R\%$ p.a.).
  • Time ($T$): The duration for which the principal money is borrowed or invested. Time MUST always be expressed in years in the SI formula.
  • Simple Interest ($SI$): The extra money paid by the borrower to the lender for using the principal money over time: $$SI = \frac{P \times R \times T}{100}$$
  • Amount ($A$): The total sum of money repaid by the borrower at the end of the loan tenure: $$A = P + SI \implies SI = A - P \implies P = A - SI$$
Target ParameterAlgebraic FormulaExample Calculation ($P=₹2000, R=5\%, T=3\text{ yr}$)
Simple Interest (SI)$SI = \frac{P \times R \times T}{100}$$SI = (2000 \times 5 \times 3) / 100 = ₹300$
Total Amount (A)$A = P + SI$$A = 2000 + 300 = ₹2,300$
Principal (P)$P = \frac{SI \times 100}{R \times T}$$P = (300 \times 100) / (5 \times 3) = ₹2,000$
Rate (R %)$R = \frac{SI \times 100}{P \times T}$$R = (300 \times 100) / (2000 \times 3) = 5\%$
Time (T years)$T = \frac{SI \times 100}{P \times R}$$T = (300 \times 100) / (2000 \times 5) = 3\text{ years}$
Cadet Mnemonic • P-R-T Formula Anchor

Remember the universal simple interest equation:

  • Principal • Rate • Time
  • Divided by 100
2. Time Conversion Protocol (Months & Days into Years)
  • Months to Years: If time is given in months ($m$), divide by 12: $$T = \frac{m}{12}\text{ years}$$ Example: 8 months $= \frac{8}{12} = \frac{2}{3}\text{ year}$; 18 months $= \frac{18}{12} = \frac{3}{2}\text{ years}$.
  • Days to Years: If time is given in days ($d$), divide by 365 (standard year): $$T = \frac{d}{365}\text{ years}$$
  • The 73-Day Factor (AISSEE Favorite): AISSEE questions almost universally use multiples of 73 days:
    • $73\text{ days} = \frac{73}{365} = \frac{1}{5}\text{ year}$
    • $146\text{ days} = \frac{146}{365} = \frac{2}{5}\text{ year}$
    • $219\text{ days} = \frac{219}{365} = \frac{3}{5}\text{ year}$
    • $292\text{ days} = \frac{292}{365} = \frac{4}{5}\text{ year}$.
Exam Trick • 73-Day Table Shortcut
Whenever days are mentioned in an AISSEE SI question, divide immediately by 73 to get the numerator over 5: 73 days = 1/5 yr, 146 days = 2/5 yr, 219 days = 3/5 yr!
AISSEE Trap Alert • The Raw Months Trap

If a loan is for 6 months at 10% p.a., using T = 6 will yield an answer 12 times too large! ALWAYS convert: T = 6/12 = 1/2 year.

3. Sum Doubling & Multiplying Shortcuts
  • Sum Doubling Rule: If a sum of money doubles itself ($A = 2P$), then the interest earned equals the principal ($SI = P$): $$P = \frac{P \times R \times T}{100} \implies R \times T = 100$$ Hence, $\text{Rate} = \frac{100}{T}$ and $\text{Time} = \frac{100}{R}$.
  • Sum Tripling Rule: If a sum triples itself ($A = 3P$), then $SI = 2P$: $$R \times T = 200 \implies T = \frac{200}{R}$$
  • Universal $n$-Times Multiplier Formula: If a sum becomes $n$ times its value at simple interest: $$R \times T = (n - 1) \times 100$$
Target GrowthInterest Earned (SI)Formula: R × TExample (at R = 10%)
Sum Doubles ($2P$)$SI = P$$R \times T = 100$$T = 100 / 10 = 10\text{ years}$
Sum Triples ($3P$)$SI = 2P$$R \times T = 200$$T = 200 / 10 = 20\text{ years}$
Sum Quadruples ($4P$)$SI = 3P$$R \times T = 300$$T = 300 / 10 = 30\text{ years}$
Sum becomes n-fold ($nP$)$SI = (n-1)P$$R \times T = (n-1) \times 100$Direct single-step solver
Visual Concept Blueprint • Vector Architecture
SIMPLE INTEREST: SI = (P × R × T) ÷ 100 | AMOUNT = P + SI • Principal (P):The initial money borrowed or invested • Rate (R%):Interest charged per ₹100 per annum (p.a.) • Time (T):Duration must always be in years (Months ÷ 12, Days ÷ 365)

Speed Shortcuts & Mental Calculation Strategies

Master these high-yield time-saving heuristics curated by top AISSEE scorers to eliminate calculation bottlenecks and answer questions in under 45 seconds.

Shortcut Technique 1: Principal directly from Amount

To find Principal directly when Amount A, Rate R, and Time T are given: $P = \frac{A \times 100}{100 + (R \times T)}$.

Shortcut Technique 2: Rate Comparison Heuristic

Simple interest grows linearly every year. If interest for 3 years is ₹600, interest for 1 year is simply ₹600 ÷ 3 = ₹200.

Shortcut Technique 3: Two Different Amounts Difference

If a sum amounts to $A_1$ in $T_1$ years and $A_2$ in $T_2$ years, the interest for $(T_2 - T_1)$ years is simply $(A_2 - A_1)$.

Interactive 3D Revision Flashcards Deck

Click any card to flip and reveal the key exam rule or topper secret.

REVISION FLASHCARD
What is the core rule & definition for Simple Interest?
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CADET MEMORY KEY
SI Formula: \text{SI} = \frac{P \times R \times T}{100}
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REVISION FLASHCARD
Cadet Shortcut: How to solve Simple Interest in under 30 seconds?
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CADET MEMORY KEY
Fast MCQ Elimination: Check the last digit (unit digit) and estimate the order of magnitude to eliminate 2 distractors in under 10 seconds.
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REVISION FLASHCARD
Exam Trap Alert: What pitfall do most candidates fall into?
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CADET MEMORY KEY
Time in Years: Time must ALWAYS be in years. 6 months = 6/12 = 1/2 year; 73 days = 73/365 = 1/5 year.
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REVISION FLASHCARD
Rapid Memory Anchor for AISSEE Hall Recall:
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CADET MEMORY KEY
Constant Interest: In simple interest, the interest earned remains constant every single year.
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REVISION FLASHCARD
What is the simple interest on ₹5,000 at 8% per annum for 73 days?
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CADET MEMORY KEY
T = 73 / 365 = 1/5 year. SI = (5000 × 8 × 1/5) / 100 = (1000 × 8) / 100 = ₹80.
Click to Flip Back
Common Traps & Examination Pitfalls

Avoid the Speed-Guess Trap: Under AISSEE pressure, candidates frequently misread units (e.g., mixing metres and centimetres, or per hour and per second) and confuse complementary ($90^\circ$) with supplementary ($180^\circ$) angles. Read every stem carefully and check units before selecting your OMR option.

Key Identities & Formulas

Simple Interest
$$SI = \frac{P \times R \times T}{100}$$
Core formula with time T strictly in years.
Total Amount
$$A = P + SI = P\left(1 + \frac{RT}{100}\right)$$
Total sum due at maturity.
Sum Doubling Rule
$$R \times T = 100$$
Time or rate for principal to double.
Step-by-Step Solved Examination Models
Solved Example 1 Model Problem
Find the simple interest and total amount on Rs 4,000 for 3 years at 6% per annum.
(A) SI = Rs 720, Amount = Rs 4,720
(B) SI = Rs 640, Amount = Rs 4,640
(C) SI = Rs 720, Amount = Rs 4,600
(D) SI = Rs 800, Amount = Rs 4,800
Detailed Solution: Formula: $\text{SI} = \frac{P \times R \times T}{100} = \frac{4000 \times 6 \times 3}{100} = 40 \times 18 = \text{Rs } 720$. Amount = $P + \text{SI} = 4000 + 720 = \text{Rs } 4,720$.
Solved Example 2 Model Problem
At what rate percent per annum will a sum of money double itself in 8 years at simple interest?
(A) 12.5%
(B) 10%
(C) 15%
(D) 8%
Detailed Solution: When money doubles, $\text{Interest} = \text{Principal } P$. $P = \frac{P \times R \times 8}{100} \implies 1 = \frac{8R}{100} \implies R = \frac{100}{8} = 12.5\%$.
Solved Example 3 Model Problem
In how many years will a sum of money double itself at 12.5% per annum simple interest?
(A) 8 years
(B) 10 years
(C) 6 years
(D) 12 years
Detailed Solution: 1. When a sum doubles itself, the Simple Interest ($SI$) equals the Principal ($P$).
2. Using the doubling formula: $R \times T = 100$.
3. Given $R = 12.5\% = \frac{25}{2}\%$.
4. $T = \frac{100}{12.5} = \frac{100 \times 2}{25} = 4 \times 2 = 8\text{ years}$. Correct Option is (A).

AISSEE High-Yield Practice Drills (10 Questions)

Simulated exam drill matching NTA question style, difficulty, and phrasing. Click an option for instant feedback and pedagogical explanation.

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Question 1 of 10 Exam Standard
Calculate the simple interest on Rs 2,500 at 8% per annum for 2 years.
Correct Answer: Option (A)
$\text{SI} = \frac{2500 \times 8 \times 2}{100} = 25 \times 16 = \text{Rs } 400$.
Question 2 of 10 Exam Standard
In how many years will Rs 1,500 amount to Rs 1,860 at 6% simple interest per annum?
Correct Answer: Option (A)
Interest = $1860 - 1500 = \text{Rs } 360$. $T = \frac{\text{SI} \times 100}{P \times R} = \frac{360 \times 100}{1500 \times 6} = \frac{36000}{9000} = 4$ years.
Question 3 of 10 Exam Standard
What principal will yield Rs 540 as simple interest in 3 years at 9% per annum?
Correct Answer: Option (A)
$P = \frac{\text{SI} \times 100}{R \times T} = \frac{540 \times 100}{9 \times 3} = \frac{54000}{27} = \text{Rs } 2,000$.
Question 4 of 10 Exam Standard
Find the rate of interest if Rs 800 amounts to Rs 1,000 in 5 years.
Correct Answer: Option (A)
Interest = $1000 - 800 = \text{Rs } 200$. $R = \frac{200 \times 100}{800 \times 5} = \frac{20000}{4000} = 5\%$.
Question 5 of 10 Exam Standard
A sum of money invested at simple interest triples itself in 10 years. What is the rate of interest?
Correct Answer: Option (A)
Triples means $\text{SI} = 2P$. $2P = \frac{P \times R \times 10}{100} \implies 2 = \frac{R}{10} \implies R = 20\%$.
Question 6 of 10 Exam Standard
Find the simple interest on Rs 5,000 at 5% per annum for 6 months.
Correct Answer: Option (A)
Time = $6/12 = 0.5$ year. $\text{SI} = \frac{5000 \times 5 \times 0.5}{100} = 50 \times 2.5 = \text{Rs } 125$.
Question 7 of 10 Exam Standard
What will be the total amount on Rs 6,500 at 10% per annum simple interest after 3 years?
Correct Answer: Option (A)
$\text{SI} = \frac{6500 \times 10 \times 3}{100} = \text{Rs } 1,950$. Amount = $6500 + 1950 = \text{Rs } 8,450$.
Question 8 of 10 Exam Standard
If the simple interest on a certain sum for 2 years at 5% per annum is Rs 100, find the interest on the same sum for 4 years at 5% per annum.
Correct Answer: Option (A)
Simple interest is directly proportional to time. When time doubles (from 2 to 4 years), interest doubles: $100 \times 2 = \text{Rs } 200$.
Question 9 of 10 Exam Standard
A farmer borrowed Rs 10,000 from a bank at 7% per annum. After 2 years, he cleared his debt by paying Rs 7,000 cash and a cow. What was the value of the cow?
Correct Answer: Option (A)
Interest = $\frac{10000 \times 7 \times 2}{100} = \text{Rs } 1,400$. Total debt = $10000 + 1400 = \text{Rs } 11,400$. Value of cow = $11,400 - 7,000 = \text{Rs } 4,400$.
Question 10 of 10 Exam Standard
At what rate of simple interest will Rs 1,200 earn an interest of Rs 288 in 3 years?
Correct Answer: Option (A)
$R = \frac{\text{SI} \times 100}{P \times T} = \frac{288 \times 100}{1200 \times 3} = \frac{28800}{3600} = 8\%$.

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Last-Minute Cadet Revision Matrix

Rapid recall checkpoints to review 24 hours before stepping into the examination hall.

Concept Checkpoint High-Yield Exam Rule & Memory Anchor
Time Unit Rule Time must ALWAYS be in years (months ÷ 12, days ÷ 365).
Linear Growth Simple interest is identical in every single year of the loan tenure.
Doubling Anchor Sum doubles when R × T = 100. Sum triples when R × T = 200.
Amount vs Interest Amount = Principal + Interest. Never confuse Amount with Simple Interest.
Frequently Asked Questions
How many questions from Simple Interest appear in the AISSEE Class VI exam?
Typically, 2 to 3 questions directly test Simple Interest in the 50-question Mathematics paper, contributing 6 to 9 marks towards the 150-mark section total.
Is there any negative marking for incorrect answers in AISSEE Class VI?
No. The National Testing Agency (NTA) does not apply negative marking in the AISSEE Class VI entrance examination. Candidates should attempt every single question.
What is the best way to revise Simple Interest before the exam?
Review the high-yield formulas, practice the 10 interactive drill MCQs on this page, and memorize the revision checkpoints matrix.