What is the difference between Simple Interest and Compound Interest?

In Simple Interest, interest is calculated only on the original principal every year. In Compound Interest, interest is added to the principal each period, so subsequent interest is earned on a growing amount. For the same P, R, and N, CI is always greater than or equal to SI.

If the rate doubles and time halves, what happens to Simple Interest?

SI = PNR/100. If R doubles (2R) and N halves (N/2), new SI = P × (N/2) × (2R) / 100 = PNR/100. The SI remains unchanged.

How do I find the principal when SI, rate, and time are given?

Use P = (100 × SI) / (N × R). For example, if SI = Rs 600, R = 5%, N = 3 years, then P = (100 × 600) / (3 × 5) = 60000 / 15 = Rs 4000.

A sum becomes 3 times itself in 10 years at SI. What is the rate?

If sum becomes 3 times, A = 3P, so SI = A - P = 2P. Using R = (100 × SI)/(P × N) = (100 × 2P)/(P × 10) = 200/10 = 20% per annum.

What does 'per annum' mean in interest problems?

Per annum means per year. When rate R is given as per annum, time N must also be in years. If time is given in months, convert: N (years) = months / 12.

Simple Interest — Formulas, Shortcuts, and Worked Examples | TNPSC, SSC, Bank

Quick Concept Summary

Simple Interest (SI) is the interest calculated on the original principal for every period of time. The interest amount is the same every year — it does not grow on accumulated interest.

Key terms you must know:

Term	Meaning
Principal (P)	The original sum of money borrowed or invested
Rate (R)	Interest charged per Rs 100 per year (% per annum)
Time (N)	Duration of the loan or investment (in years)
Simple Interest (SI)	The interest earned/paid on the principal
Amount (A)	Total money returned = Principal + SI

When to use Simple Interest: Bank loans for short periods, government schemes like Post Office Savings, hire-purchase agreements, and most TNPSC/SSC aptitude problems unless stated otherwise.

Key Formulas

What to Find	Formula
Simple Interest	SI = (P × N × R) / 100
Amount	A = P + SI
Principal	P = (100 × SI) / (N × R)
Rate	R = (100 × SI) / (P × N)
Time	N = (100 × SI) / (P × R)
Principal from Amount	P = (100 × A) / (100 + N × R)
Rate when amount is given	R = [(A/P) - 1] × (100/N)

Important derived relationships:

If a sum becomes k times in N years at SI, then R = (k - 1) × 100 / N
If a sum doubles (k = 2): R = 100/N
If a sum triples (k = 3): R = 200/N

Worked Examples

Example 1: Find SI and Amount (Basic)

Problem:
Find the Simple Interest and Amount on Rs 8,000 at 6% per annum for 3 years.

Given:
  P = Rs 8,000
  R = 6% per annum
  N = 3 years

Step 1: Apply the SI formula
  SI = (P × N × R) / 100
  SI = (8000 × 3 × 6) / 100
  SI = 144000 / 100
  SI = Rs 1,440

Step 2: Calculate Amount
  A = P + SI
  A = 8000 + 1440
  A = Rs 9,440

Answer: Simple Interest = Rs 1,440 | Amount = Rs 9,440

Example 2: Find the Rate of Interest

Problem:
A principal of Rs 5,000 yields Rs 1,500 as Simple Interest in 5 years.
Find the rate of interest per annum.

Given:
  P = Rs 5,000
  SI = Rs 1,500
  N = 5 years
  R = ?

Step 1: Apply the rate formula
  R = (100 × SI) / (P × N)
  R = (100 × 1500) / (5000 × 5)
  R = 150000 / 25000
  R = 6% per annum

Answer: Rate of Interest = 6% per annum

Example 3: Find the Principal

Problem:
At 8% per annum Simple Interest, a sum of money amounts to Rs 7,200 in 4 years.
Find the principal.

Given:
  A = Rs 7,200
  R = 8% per annum
  N = 4 years
  P = ?

Step 1: Use the principal from amount formula
  P = (100 × A) / (100 + N × R)
  P = (100 × 7200) / (100 + 4 × 8)
  P = 720000 / (100 + 32)
  P = 720000 / 132
  P = Rs 5,454.54

Alternative method:
  Let P = principal
  SI = A - P = 7200 - P
  Also, SI = P × 4 × 8 / 100 = 32P/100

  So: 7200 - P = 32P/100
  Multiply both sides by 100:
  720000 - 100P = 32P
  720000 = 132P
  P = 720000 / 132 = Rs 5,454.54

Answer: Principal = Rs 5,454.54 (approximately Rs 5,455)

Example 4: Find Time (given SI and other values)

Problem:
In how many years will Rs 4,500 amount to Rs 5,850 at Simple Interest of 6% per annum?

Given:
  P = Rs 4,500
  A = Rs 5,850
  R = 6%
  N = ?

Step 1: Find SI
  SI = A - P = 5850 - 4500 = Rs 1,350

Step 2: Apply time formula
  N = (100 × SI) / (P × R)
  N = (100 × 1350) / (4500 × 6)
  N = 135000 / 27000
  N = 5 years

Answer: Time = 5 years

Example 5: A Sum Becomes Multiple Times (Rate Calculation)

Problem:
At Simple Interest, a sum of money doubles itself in 8 years.
In how many years will it become 5 times?

Step 1: Find the rate using "sum doubles in 8 years"
  When sum doubles: SI = P (interest earned = original principal)
  N = (100 × SI) / (P × R)
  8 = (100 × P) / (P × R)
  8 = 100 / R
  R = 100/8 = 12.5% per annum

Step 2: Find time for sum to become 5 times
  When sum becomes 5 times: A = 5P, so SI = 4P
  N = (100 × SI) / (P × R)
  N = (100 × 4P) / (P × 12.5)
  N = 400P / (12.5P)
  N = 400 / 12.5
  N = 32 years

Shortcut: If sum doubles in T years, it becomes k times in T(k-1) years.
  Doubles in 8 years → 5 times in 8 × (5-1) = 8 × 4 = 32 years ✓

Answer: The sum becomes 5 times in 32 years.

Example 6: Two Parts Invested at Different Rates

Problem:
Rs 12,000 is split into two parts. One part is invested at 5% SI and the other
at 8% SI. After 2 years, the total interest earned is Rs 1,560. Find each part.

Given:
  Total principal = Rs 12,000
  Let Part 1 = Rs x at 5% for 2 years
  Let Part 2 = Rs (12000 - x) at 8% for 2 years
  Total SI = Rs 1,560

Step 1: Write the SI equation
  SI from Part 1 = (x × 2 × 5) / 100 = 10x/100 = x/10
  SI from Part 2 = ((12000 - x) × 2 × 8) / 100 = 16(12000 - x)/100

Step 2: Set up the equation
  x/10 + 16(12000 - x)/100 = 1560

  Multiply everything by 100:
  10x + 16(12000 - x) = 156000
  10x + 192000 - 16x = 156000
  -6x = 156000 - 192000
  -6x = -36000
  x = 6000

Step 3: Find both parts
  Part 1 = Rs 6,000 at 5%
  Part 2 = Rs 12,000 - Rs 6,000 = Rs 6,000 at 8%

Verification:
  SI from Part 1 = (6000 × 2 × 5)/100 = Rs 600
  SI from Part 2 = (6000 × 2 × 8)/100 = Rs 960
  Total = 600 + 960 = Rs 1,560 ✓

Answer: Each part = Rs 6,000

Shortcuts and Tricks

Trick 1: The Multiple Times Shortcut

If a sum doubles in N years at SI:

Triples in 2N years
Becomes 4 times in 3N years
Becomes k times in (k-1) × N years

Example: Doubles in 5 years → triples in 10 years, quadruples in 15 years.

Trick 2: Rate–Time Interchange

If R and N are swapped (rate becomes time and time becomes rate), the SI remains the same.

Example: P = 1000, R = 4%, N = 6 years → SI = (1000 × 4 × 6)/100 = 240 Same: P = 1000, R = 6%, N = 4 years → SI = (1000 × 6 × 4)/100 = 240 ✓

Trick 3: Percentage Shortcut for Quick SI

Convert the rate-time product into a percentage directly:

SI % = R × N (this is the % of principal that becomes interest)
SI = P × (R × N) / 100

Example: P = 5000, R = 7%, N = 4 years SI % = 7 × 4 = 28% SI = 5000 × 28/100 = Rs 1,400

Trick 4: Finding Principal When Amount and SI % are Known

If you know that a sum amounts to Rs A at x% SI over N years: P = A × 100 / (100 + R×N)

Example: Amount = Rs 7,600, R = 8%, N = 5 years P = 7600 × 100 / (100 + 40) = 760000 / 140 = Rs 5,428.57

Trick 5: SI Difference Between Two Rates

When the same principal P is invested for the same time N but at two different rates R1 and R2: Difference in SI = P × N × (R2 - R1) / 100

Example: Rs 10,000 for 3 years at 7% vs 9% SI difference = 10000 × 3 × (9-7) / 100 = 10000 × 3 × 2 / 100 = Rs 600

TNPSC Exam Pattern

How Simple Interest appears in TNPSC Group 2, Group 4, and VAO exams:

Question Type	Frequency	Difficulty
Find SI given P, R, N	Very common	Easy
Find Rate given P, SI, N	Common	Easy–Medium
Find Principal given A, R, N	Common	Medium
A sum becomes k times — find R or N	Common	Medium
Two sums invested at different rates	Occasional	Medium
SI vs CI difference (first 2 years)	Occasional	Medium

Key exam points:

Always check if time is given in months — convert to years (divide by 12)
TNPSC often gives amounts (A) rather than SI — remember SI = A - P
Watch for "per annum" vs "per month" — most problems are per annum
If rate is "half-yearly," double it to get annual rate for SI problems (SI doesn't compound)
Expected 2–3 SI questions in TNPSC Preliminary exam

Practice Questions

Q1. Find the Simple Interest on Rs 6,000 at 5% per annum for 4 years. Answer: SI = (6000 × 4 × 5)/100 = Rs 1,200

Q2. What is the amount when Rs 3,500 is invested at 7% SI for 3 years? Answer: SI = (3500 × 3 × 7)/100 = Rs 735. Amount = 3500 + 735 = Rs 4,235

Q3. At what rate will Rs 2,000 yield Rs 400 as SI in 4 years? Answer: R = (100 × 400)/(2000 × 4) = 40000/8000 = 5% per annum

Q4. In how many years will Rs 1,500 earn Rs 270 at 6% per annum SI? Answer: N = (100 × 270)/(1500 × 6) = 27000/9000 = 3 years

Q5. A sum of Rs 4,000 amounts to Rs 5,200 in 4 years at SI. Find the rate. Answer: SI = 5200 - 4000 = 1200. R = (100 × 1200)/(4000 × 4) = 120000/16000 = 7.5% per annum

Q6. A principal doubles itself in 12 years at SI. In how many years will it become 5 times? Answer: Using shortcut: doubles in 12 years → 5 times in (5-1) × 12 = 48 years

Q7. Find the principal that gives Rs 900 as SI at 9% per annum in 5 years. Answer: P = (100 × 900)/(5 × 9) = 90000/45 = Rs 2,000

Q8. Rs 10,000 is invested partly at 6% and partly at 9% for 2 years. If total SI = Rs 1,500, find the amount invested at 6%. Answer: Let x at 6%. SI: (x×2×6)/100 + ((10000-x)×2×9)/100 = 1500 → 12x + 18(10000-x) = 150000 → 12x + 180000 - 18x = 150000 → -6x = -30000 → x = 5000. Rs 5,000 at 6%.

Q9. The difference in SI on Rs 8,000 for 3 years at two different rates is Rs 240. Find the difference in rates. Answer: Difference in SI = P × N × (R2 - R1)/100 → 240 = 8000 × 3 × (R2-R1)/100 → (R2-R1) = 24000/24000 = 1% per annum

Q10. What sum of money will amount to Rs 9,600 in 3 years at 8% per annum SI? Answer: P = (100 × 9600)/(100 + 3×8) = 960000/124 = Rs 7,741.94 ≈ Rs 7,742