SSC MATH PYQ QUIZ: COMPOUND INTEREST

Solution:

1. Given Data:

• Compound Interest (CI) = ₹840

• Principal (P) = ₹4,000

• Time (T) = 2 years

• Rate of Interest (R) = ?

2. Find Total Amount (A): Amount = Principal + Compound Interest A = 4000 + 840 A = ₹4,840

3. Formula: The formula for the total amount (A) under compound interest is: A = P * (1 + R / 100)^T

4. Calculation: Substitute the given values into the formula: 4840 = 4000 * (1 + R / 100)^2

Divide both sides by 4,000: 4840 / 4000 = (1 + R / 100)^2

Simplify the fraction on the left side (divide numerator and denominator by 40): 121 / 100 = (1 + R / 100)^2

Write both sides in square form: (11 / 10)^2 = (1 + R / 100)^2

Taking square root on both sides: 11 / 10 = 1 + R / 100

Subtract 1 from both sides: (11 / 10) - 1 = R / 100 (11 - 10) / 10 = R / 100 1 / 10 = R / 100

Solve for R: R = (100 / 10) = 10

5. Final Answer: The rate of interest is 10% per annum.

Solution:

1. Given Data:

• Initial Value (P) = ₹25,000

• Rate of Depreciation (R) = 20% per annum

• Time (T) = 2 years

2. Formula: Since the value decreases (depreciates) over time, the formula is: A = P * (1 - R / 100)^T

3. Calculation: Substitute the given values into the formula: A = 25000 * (1 - 20 / 100)^2

Simplify the fraction inside the bracket: A = 25000 * (1 - 1 / 5)^2 A = 25000 * (4 / 5)^2

Calculate the square: A = 25000 * (16 / 25)

Divide 25,000 by 25: A = 1000 * 16 A = ₹16,000

4. Final Answer: The value of the machine after 2 years will be ₹16,000.

Step-by-Step Solution

1. Given Data:

• Principal ($P$) = ₹10,000

• Rate of Interest ($R$) = 10% per annum

• Time ($T$) = 2 years

2. Formula:

The formula for finding the total amount ($A$) under compound interest is:

3. Calculation:

Substitute the given values into the formula:

Simplify the fraction inside the bracket:

Calculate the square:

4. Final Answer:

• The total amount after 2 years is ₹12,100.

• (If needed, the Compound Interest is $\text{₹}12,100-\text{₹}10,000=\text{₹}2,100$)

Case 1: Simple Interest (SI) ke anusar

• Principal ($P$) = $P$

• Amount ($A$) = $3P$ (Matlab sum triple ho gaya)

• Simple Interest ($SI$) = $3P-P=2P$

• Time ($T$) = 2 years

Formula:

Values put karein:

Case 2: Compound Interest (CI) ke anusar

• Principal ($P$) = $P$

• Amount ($A$) = $3P$

• Time ($n$) = 2 years

Formula:

Values put karein:

Dono taraf square root lene par:

Kyunki 3<img class="katex-svg" src="data:;base64,​≈1.732 hota hai:

Step-by-Step Solution

1. Given Data:

• Principal ($P$) = ₹5,000

• Rate of Interest ($R$) = 10% per annum

• Time ($T$) = 2 years

2. Formula:

The formula for finding the total amount ($A$) under compound interest is:

And Compound Interest ($CI$) is calculated as:

3. Calculation:

First, calculate the total amount ($A$):

Simplify the fraction inside the bracket:

Calculate the square:

Now, find the Compound Interest ($CI$):

4. Final Answer:

• The compound interest is ₹1,050 (and the total amount after 2 years is ₹6,050).

Diye Gaye Ankr (Given Data):

• Principal ($P$): ₹3,000

• Rate ($R$): 10% per annum

• Time ($n$ ya $T$): 2 years

Method 1: Direct Formula (2 saal ke liye sabse aasan tarika)

2 saal ke liye Compound Interest (CI) aur Simple Interest (SI) ka antar (Difference) nikalne ka direct formula hota hai:

Values put karein:

Method 2: Alag-alag nikal kar (Step-by-Step)

1. Simple Interest (SI) nikalen:

2. Compound Interest (CI) nikalen:

3. Antar (Difference) nikalen:

Answer: CI aur SI ka antar ₹30 hai.

Solution:

1. Given Data:

• Initial Value of the car (P) = ₹1,00,000

• Rate of Depreciation (R) = 20% per annum

• Time (T) = 2 years

2. Formula: Since the value decreases (depreciates) over time, the formula is: A = P * (1 - R / 100)^T

3. Calculation: Substitute the given values into the formula: A = 100000 * (1 - 20 / 100)^2

Simplify the fraction inside the bracket: A = 100000 * (1 - 1 / 5)^2 A = 100000 * (4 / 5)^2

Calculate the square: A = 100000 * (16 / 25)

Divide 100000 by 25: A = 4000 * 16

A = ₹64,000

4. Final Answer: The value of the car after 2 years will be ₹64,000.

Step-by-Step Solution

1. Given Data:

• Initial Value of the Machine ($P$) = ₹50,000

• Rate of Depreciation ($R$) = 10% per annum

• Time ($T$) = 2 years

2. Formula:

Since the value decreases (depreciates) over time, the formula used is:

3. Calculation:

Substitute the given values into the formula:

Simplify the fraction inside the bracket:

Calculate the square:

Divide $50,000$ by $100$:

4. Final Answer:

• The value of the machine after 2 years will be ₹40,500.

Solution:

1. Given Data:

• Let the initial principal be P.

• Amount (A) after 3 years = 2P (since the sum doubles)

• Time (T) = 3 years

2. Formula: A = P * (1 + R / 100)^T

3. Calculation: Substitute the values into the formula: 2P = P * (1 + R / 100)^3

Divide both sides by P: 2 = (1 + R / 100)^3

Taking cube root on both sides: (2)^(1/3) = 1 + R / 100

Subtract 1 from both sides: (2)^(1/3) - 1 = R / 100

Multiply by 100 to find R: R = 100 * ((2)^(1/3) - 1)

4. Final Answer: The rate of interest is 100 * ((2)^(1/3) - 1)% per annum (approximately 25.99% or 26%).

Compound Interest (CI) Calculation

Given Data:

• Principal ($P$): ₹6,000

• Rate ($R$): 10% per annum

• Time ($n$): 3 years

Method 1: Using the Formula

The formula for the total Amount ($A$) in compound interest is:

Substitute the given values into the formula:

Now, calculate the Compound Interest ($CI$):

Method 2: Year-by-Year Calculation (Simple & Intuitive)

• 1st Year:

  • Interest = 10% of ₹6,000 = ₹600

  • Amount at the end of Year 1 = ₹6,000 + ₹600 = ₹6,600

• 2nd Year:

  • Interest = 10% of ₹6,600 = ₹660

  • Amount at the end of Year 2 = ₹6,600 + ₹660 = ₹7,260

• 3rd Year:

  • Interest = 10% of ₹7,260 = ₹726

  • Amount at the end of Year 3 = ₹7,260 + ₹726 = ₹7,986

• Total Compound Interest:

  • $CI=600+660+726=$ ₹1,986

Answer: The Compound Interest is ₹1,986.

Step-by-Step Solution

1. Given Data:

• Present Population ($P$) = $20,000$

• Rate of Increase ($R$) = $5\%$ per annum

• Time ($T$) = $2$ years

2. Formula:

The formula for population growth after $T$ years (similar to compound interest) is:

3. Calculation:

Substitute the given values into the formula:

Simplify the fraction inside the bracket:

Calculate the square:

Divide $20,000$ by $400$:

4. Final Answer:

• The population of the town after 2 years will be 22,050.

• Shuruat ki Population = 40,000

• 2 saal baad ki Population = 44,100

• Samay (Time) = 2 saal

Step 1: Dono ka anupat (Ratio) nikalein: Ratio = 44,100 / 40,000 Ratio = 441 / 400

Step 2: Kyunki samay 2 saal hai, isliye iska vargmul (Square Root) nikalein: Square Root of (441 / 400) = 21 / 20

Iska matlab yeh hai ki agar 1 saal mein population 20 thi, toh badhkar 21 ho gayi.

Step 3: Pratishat (Rate) nikalein:

• 20 par kitni badhotri hui? -> 21 - 20 = 1 ki badhotri

• Rate (%) = (1 / 20) * 100 = 5%

Answer: Rate = 5% per annum

Solution:

1. Given Data:

• Amount (A) = ₹13,310

• Rate of Interest (R) = 10% per annum

• Time (T) = 2 years

• Principal (P) = ?

2. Formula: The formula for the total amount (A) under compound interest is: A = P * (1 + R / 100)^T

3. Calculation: Substitute the given values into the formula: 13310 = P * (1 + 10 / 100)^2

Simplify the fraction inside the bracket: 13310 = P * (1 + 1 / 10)^2 13310 = P * (11 / 10)^2

Calculate the square: 13310 = P * (121 / 100)

Solve for P: P = (13310 * 100) / 121

Divide 13,310 by 121: P = 110 * 100 P = ₹11,000

4. Final Answer: The principal amount is ₹11,000.

Step-by-Step Solution

1. Given Data:

• Principal ($P$) = ₹2,000

• Rate of Interest ($R$) = 10% per annum

• Time ($T$) = 2 years

2. Calculate Simple Interest (SI):

The formula for Simple Interest is:

3. Calculate Compound Interest (CI):

The formula for the total Amount ($A$) under compound interest is:

Now, calculate Compound Interest ($CI$):

4. Find the Difference:

(Note: For 2 years, you can also use the direct shortcut formula for the difference between CI and SI: Difference=1002P×R2​=100002000×102​=100002000×100​=₹20)

5. Final Answer:

• The difference between Compound Interest and Simple Interest is ₹20.