Simple & Compound Interest
Key Concepts & Formulas
Provide 5-7 essential concepts for Simple & Compound Interest:
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Principal (P) | The initial amount of money invested or borrowed |
| 2 | Rate (R) | Annual interest rate expressed as a percentage |
| 3 | Time (T) | Duration for which money is invested/borrowed (in years) |
| 4 | Amount (A) | Total money received after interest (Principal + Interest) |
| 5 | Compounding Frequency | How often interest is calculated - yearly, half-yearly, quarterly |
| 6 | Effective Rate | Actual annual rate when compounding occurs multiple times per year |
| 7 | Difference Formula | CI - SI = P(R/100)² for 2 years (useful shortcut) |
Essential Formulas
| Formula | Usage |
|---|---|
| SI = PRT/100 | [When to use] Calculate simple interest when principal, rate, and time are known |
| A = P(1+R/100)^T | [When to use] Find compound amount when compounding annually |
| CI = A - P | [When to use] Calculate compound interest after finding amount |
| A = P(1+R/200)^(2T) | [When to use] Compound interest when compounding half-yearly |
| A = P(1+R/400)^(4T) | [When to use] Compound interest when compounding quarterly |
10 Practice MCQs
Q1. A railway employee deposits ₹15,000 in a savings scheme for 3 years at 8% simple interest per annum. What is the total interest earned? A) ₹3,200 B) ₹3,600 C) ₹3,800 D) ₹4,000
Answer: B) ₹3,600
Solution: SI = PRT/100 = 15000 × 8 × 3 / 100 = ₹3,600
Shortcut: Calculate 8% of 15000 = 1200, then multiply by 3 years = 3600
Concept: Simple & Compound Interest - Simple Interest calculation
Q2. Find the compound interest on ₹20,000 for 2 years at 10% per annum compounded annually. A) ₹4,000 B) ₹4,200 C) ₹4,400 D) ₹4,600
Answer: B) ₹4,200
Solution: A = P(1+R/100)^T = 20000(1+10/100)² = 20000 × 1.21 = ₹24,200 CI = A - P = 24,200 - 20,000 = ₹4,200
Shortcut: Use 10% compound interest factor for 2 years = 21% of principal
Concept: Simple & Compound Interest - Compound Interest calculation
Q3. The difference between compound interest and simple interest on a certain sum for 2 years at 5% per annum is ₹50. Find the principal. A) ₹10,000 B) ₹15,000 C) ₹20,000 D) ₹25,000
Answer: C) ₹20,000
Solution: CI - SI = P(R/100)² 50 = P(5/100)² = P(25/10000) P = 50 × 10000/25 = ₹20,000
Shortcut: Direct formula application
Concept: Simple & Compound Interest - Difference formula
Q4. A train ticket costs ₹1,200. If booked 30 days in advance with 2% simple interest discount, what is the final amount paid? A) ₹1,176 B) ₹1,180 C) ₹1,184 D) ₹1,192
Answer: A) ₹1,176
Solution: Discount = S.I. = PRT/100 = 1200 × 2 × 1/12 / 100 = ₹24 (1 month = 1/12 year) Final Amount = 1200 - 24 = ₹1,176
Shortcut: Calculate 2% of monthly amount = 0.166% of 1200
Concept: Simple & Compound Interest - Time conversion
Q5. A railway workshop invests ₹50,000 at 12% compound interest compounded half-yearly for 1 year. Find the maturity amount. A) ₹56,000 B) ₹56,180 C) ₹56,360 D) ₹56,720
Answer: B) ₹56,180
Solution: For half-yearly: R = 12/2 = 6%, T = 1 × 2 = 2 periods A = P(1+R/100)^T = 50000(1+6/100)² = 50000 × 1.1236 = ₹56,180
Shortcut: 6% compound for 2 periods ≈ 12.36% effective
Concept: Simple & Compound Interest - Half-yearly compounding
Q6. The simple interest on a sum for 3 years at 8% is ₹3,600. What would be the compound interest for the same sum and rate for 2 years? A) ₹2,496 B) ₹2,596 C) ₹2,696 D) ₹2,796
Answer: A) ₹2,496
Solution: First find P: 3600 = P × 8 × 3 / 100 → P = ₹15,000 Then CI: A = 15000(1+8/100)² = 15000 × 1.1664 = ₹17,496 CI = 17,496 - 15,000 = ₹2,496
Shortcut: Use SI to find P, then compound formula
Concept: Simple & Compound Interest - Mixed calculations
Q7. A sum becomes 3 times itself in 15 years at simple interest. In how many years will it become 5 times? A) 25 B) 30 C) 35 D) 40
Answer: B) 30
Solution: 3P = P + SI → SI = 2P 2P = P × R × 15 / 100 → R = 40/3% For 5 times: 4P = P × 40/3 × T / 100 → T = 30 years
Shortcut: Time is directly proportional to multiple when rate is constant
Concept: Simple & Compound Interest - Proportionality
Q8. If the difference between CI and SI for 3 years at 10% is ₹1,550, find the principal. A) ₹40,000 B) ₹45,000 C) ₹50,000 D) ₹55,000
Answer: C) ₹50,000
Solution: For 3 years: CI - SI = P[(1+R/100)³ - 1 - 3R/100] 1550 = P[(1.1)³ - 1 - 0.3] = P[1.331 - 1.3] = P × 0.031 P = 1550/0.031 = ₹50,000
Shortcut: Use compound difference formula for 3 years
Concept: Simple & Compound Interest - Advanced difference formula
Q9. A railway employee borrows ₹1,00,000 at 12% compound interest for 2 years, but pays simple interest for the first year and compound for the second. Find total interest. A) ₹25,440 B) ₹26,400 C) ₹27,200 D) ₹28,160
Answer: A) ₹25,440
Solution: Year 1 SI: 100000 × 12 × 1 / 100 = ₹12,000 Principal for Year 2: ₹100,000 Year 2 CI: 100000 × 12/100 = ₹12,000 But on ₹112,000: 112000 × 12/100 = ₹13,440 Total = 12,000 + 13,440 = ₹25,440
Shortcut: Calculate year-wise separately
Concept: Simple & Compound Interest - Mixed interest type
Q10. Two equal sums are invested at 10% simple interest and 10% compound interest. After 2 years, the compound interest exceeds simple interest by ₹100. Find each sum. A) ₹8,000 B) ₹10,000 C) ₹12,000 D) ₹15,000
Answer: B) ₹10,000
Solution: CI - SI = P(R/100)² 100 = P(10/100)² = P/100 P = ₹10,000
Shortcut: Direct application of difference formula
Concept: Simple & Compound Interest - Comparative analysis
5 Previous Year Questions
PYQ 1. A sum of money doubles itself in 8 years at simple interest. What is the rate of interest? [RRB NTPC 2021 CBT-1]
Answer: C) 12.5%
Solution: P = SI → P = P × R × 8 / 100 → R = 100/8 = 12.5%
Exam Tip: When money doubles, SI equals Principal. Use this relationship.
PYQ 2. The compound interest on ₹8,000 for 2 years at 5% per annum is: [RRB Group D 2022]
Answer: B) ₹820
Solution: A = 8000(1+5/100)² = 8000 × 1.1025 = ₹8,820 CI = 8820 - 8000 = ₹820
Exam Tip: Always subtract principal from amount to get CI.
PYQ 3. A certain sum amounts to ₹6,600 in 4 years and ₹7,200 in 5 years at simple interest. Find the rate of interest. [RRB ALP 2018]
Answer: A) 10%
Solution: SI for 1 year = 7200 - 6600 = ₹600 SI for 4 years = 600 × 4 = ₹2,400 Principal = 6600 - 2400 = ₹4,200 Rate = (600 × 100)/(4200 × 1) = 10%
Exam Tip: Difference between consecutive years gives annual SI.
PYQ 4. If the compound interest on a certain sum for 2 years at 4% is ₹1,632, find the simple interest for double the time and half the rate. [RRB JE 2019]
Answer: D) ₹3,200
Solution: First find P: 1632 = P[(1.04)² - 1] → P = ₹20,000 New conditions: T = 4 years, R = 2% SI = 20000 × 2 × 4 / 100 = ₹1,600
Exam Tip: Always find principal first, then apply new conditions.
PYQ 5. A train ticket costs ₹1,500. If 10% simple interest is charged for paying after 3 months, what is the total amount to be paid? [RPF SI 2019]
Answer: B) ₹1,537.50
Solution: SI = 1500 × 10 × 3/12 / 100 = ₹37.50 Total = 1500 + 37.50 = ₹1,537.50
Exam Tip: Convert months to years (3 months = 0.25 years).
Speed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| Money doubles in SI | Rate = 100/Time | If 8 years → Rate = 12.5% |
| CI for 2 years at 10% | Multiply by 0.21 | ₹5000 → CI = 5000 × 0.21 = ₹1050 |
| Half-yearly compounding | Double time, half rate | 12% annual → 6% half-yearly |
| Quarterly compounding | 4× time, ¼ rate | 12% annual → 3% quarterly |
| SI to CI conversion | Use factor tables | Memorize (1.1)²=1.21, (1.2)²=1.44 |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Not converting time units | Assuming all time given in years | Always check if months/days given |
| Using wrong compounding formula | Confusing annual with half-yearly | Adjust rate and time according to frequency |
| Calculating CI directly | Trying to find CI without finding amount | Always find A = P(1+R/100)^T first |
| Rounding intermediate values | Rounding before final answer | Keep full precision until final step |
| Ignoring leap years | Not accounting for exact days | Use 365 days for accuracy when needed |
Quick Revision Flashcards
| Front (Question/Term) | Back (Answer) |
|---|---|
| SI Formula | PRT/100 |
| CI Formula | P(1+R/100)^T - P |
| Time conversion | 1 month = 1/12 year |
| Half-yearly rate | Annual rate ÷ 2 |
| Quarterly rate | Annual rate ÷ 4 |
| Money doubles SI | Rate × Time = 100 |
| CI-SI difference (2 years) | P(R/100)² |
| Effective annual rate | Higher than nominal with compounding |
| Compound interest factor | (1+R/100)^T |
| Simple interest factor | RT/100 |
Topic Connections
How Simple & Compound Interest connects to other RRB exam topics:
- Direct Link: Percentages - Interest rates are percentages; mastery of percentage calculations essential
- Combined Questions: Ratio & Proportion - Often mixed with partnership problems and investment ratios
- Foundation For: Data Interpretation - Bank interest tables, investment growth charts in DI sets
- Common Pattern: Time & Work - Similar concept of rate × time = work done
- Extension: Profit & Loss - Interest calculations form basis of financial mathematics
BETA
