Simple and Compound Both MCQ Quiz - Objective Question with Answer for Simple and Compound Both - Download Free PDF

Last updated on Jun 3, 2025

Simple and Compound Question and Answers are a highly scoring section in the Quantitative Aptitude subject. Simple and Compound MCQs Quiz are an important component of government entrance exams such as Bank PO, IBPS PO, SBI PO, RRB PO, RBI Assistant, LIC,SSC, MBA - MAT, XAT, CAT, NMAT, UPSC, NET etc. This section has practice questions for Simple and Compound Both Objective Questions. Practice well and ace your exam.

Latest Simple and Compound Both MCQ Objective Questions

Simple and Compound Both Question 1:

P invests Rs (X − 5000) at a compound interest rate of R% per annum for 2 years, while Q invests Rs (X + 2000) at 2R% per annum for the same period. The ratio of their investments is given to be 5 : 7. Find the difference in the compound interest earned by A and B after 2 years.

  1. 2400
  2. 12400
  3. 5600
  4. Can’t be determined
  5. None of these

Answer (Detailed Solution Below)

Option 4 : Can’t be determined

Simple and Compound Both Question 1 Detailed Solution

Calculation

So, [ X – 5000] / [ X + 2000] = 5 /7

Or, 5𝑋 + 10000 = 7X – 35000

Or, 2𝑋 = 45000

Or, 𝑋 = 22500

So, Investment of P and Q is Rs 17500 and Rs 24500 respectively.

We don’t know the value of R So, answer can’t be determined.

(d) Can’t be determined

Simple and Compound Both Question 2:

A principal amount is invested at 12% per annum simple interest for a period of 4 years, 11 months, and 28 days in a scheme. The total amount received from this scheme is then invested for 2 years and 2 days in another scheme at 20% per annum compound interest. The compound interest earned from the second scheme is Rs. 1056.4. Find the approximate amount initially invested in the first scheme?

  1. 1950
  2. 1850
  3. 1450
  4. 1650
  5. 1500

Answer (Detailed Solution Below)

Option 5 : 1500

Simple and Compound Both Question 2 Detailed Solution

Calculation

We should take approx. values

So, four years 11 months and 28 days = 5 years

Two years 2 days = 2 years

And 1056.4 Rs = 1056

Equivalent rate of interest at rate of 20% p.a. for two years on compound

interest annually = (20 + 20 + ( 20 × 20) / 100 )% = 44%

Let amount invested in first scheme = 100x

So, amount invested in second scheme = 100x + 100x × (12× 5) /100

= 160x 

ATQ, 160x × (44 / 100) = 1056

Or, 1.6x = 24

x = 15

So, 100x = 1500

Simple and Compound Both Question 3:

Simple interest received on a certain sum at a rate of simple interest of 5% for 2 years is Rs.780. If the rate of interest remains same, what will be the total amount at the time of withdrawal at the end of 5 years.

 

  1. 9750
  2. 9250
  3. 9650
  4. 9450
  5. 9950

Answer (Detailed Solution Below)

Option 1 : 9750

Simple and Compound Both Question 3 Detailed Solution

Calculation

We use the simple interest formula:
SI = (P × R × T)/100

Given:
SI = 780, R = 5%, T = 2
→ 780=P×5×2100
→ P=780×100/10=7800

Now SI for 5 years:
→ SI=7800×5×5/100=1950
Total amount = Principal + SI = 7800 + 1950 = Rs.9750

Simple and Compound Both Question 4:

A sum amounts to ₹ 9075 in \(1\frac{1}{3}\) years at 15% p.a. compounded 8-monthly. What is the simple interest (in ₹) on the same sum for the same period and at the same rate of interest ?

  1. 1200
  2. 1250
  3. 1500
  4. 1550

Answer (Detailed Solution Below)

Option 3 : 1500

Simple and Compound Both Question 4 Detailed Solution

Given:

Amount (A) = ₹ 9075

Time (T) = 1 and 1/3 years = 4/3 years

Rate of interest (R) = 15% p.a.

Compounded 8-monthly

Formula used:

For compound interest: A = P(1 + r/100)n, where:

A = Amount

P = Principal

r = Rate of interest per compounding period

n = Number of compounding periods

Calculation:

First, calculate the number of compounding periods (n) and the rate per compounding period (r).

Time in months = (4/3) years × 12 months/year = 16 months

Compounding period = 8 months

Number of compounding periods (n) = Total months / Compounding period = 16 / 8 = 2 periods

Annual rate = 15%

Rate per month = 15% / 12 = 5/4 %

Rate per 8-monthly period (r) = (5/4) % × 8 = 10%

Now, use the compound interest formula to find the Principal (P):

A = P(1 + r/100)n

9075 = P(1 + 10/100)2

9075 = P(1 + 1/10)2

9075 = P(11/10)2

9075 = P(121/100)

P = (9075 × 100) / 121

P = 75 × 100

P = ₹ 7500

SI on the same sum (P = ₹ 7500) for the same period (T = 4/3 years) and at the same rate (R = 15% p.a.).

SI = (P × R × T) / 100

SI = (7500 × 15 × (4/3)) / 100

SI = (7500 × 15 × 4) / (3 × 100)

SI = (75 × 15 × 4) / 3

SI = 25 × 15 × 4

SI = 25 × 60

SI = ₹ 1500

∴ The correct answer is option 3.

Simple and Compound Both Question 5:

The difference between compound interest and simple interest on an amount of money in three years at the rate of 8% is Rs. 3,456. Then the principal amount is

  1. Rs. 1,75,325
  2.  Rs. 5,00,000 
  3. Rs. 3,50,000
  4. Rs. 4,00,000

Answer (Detailed Solution Below)

Option 1 : Rs. 1,75,325

Simple and Compound Both Question 5 Detailed Solution

Given:

Difference between CI and SI for 3 years = ₹3,456

Rate of interest (r) = 8% per annum

Time (t) = 3 years

Formula Used:

Difference between CI and SI for 3 years = P × (r/100)2 × (3 + r/100)

Where P is the principal.

Calculation:

Substitute the given values into the formula:

3456 = P × (8/100)2 × (3 + 8/100)

3456 = P × (0.08)2 × (3 + 0.08)

3456 = P × 0.0064 × 3.08

3456 = P × 0.019712

P = 3456 / 0.019712

P = 175324.625 ≈ 175325

∴ The principal amount is approximately ₹175,325.

Top Simple and Compound Both MCQ Objective Questions

On a certain sum of money, the compound interest for 2 years is Rs. 304.5 and the simple interest for the same period of time is Rs. 290. The rate of interest per annum:

  1. 9%
  2. 8%
  3. 11%
  4. 10%

Answer (Detailed Solution Below)

Option 4 : 10%

Simple and Compound Both Question 6 Detailed Solution

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Given:

C.I for 2 years = Rs. 304.5

S.I for 2 years = Rs. 290

Calculation:

S.I for 1 year = Rs. (290/2) = Rs. 145

Difference between S.I and C.I = Rs. (304.5 – 290)

⇒ Rs. 14.5

Rate of interest per annum = (14.5/145) × 100%

⇒ 10%

∴ The rate of interest per annum is 10%

Find the principal if the interest compounded at the rate of 12% per annum, compounding annually for 2 years is Rs. 1,908.

  1. Rs. 6,500
  2. Rs. 5,400
  3. Rs. 7,500
  4. Rs. 4,500

Answer (Detailed Solution Below)

Option 3 : Rs. 7,500

Simple and Compound Both Question 7 Detailed Solution

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Given

Compound interest after 2 years = Rs. 1,908

Rate of interest = 12% per annum

Concept:

CI = P [(1 + r/100)t - 1]

Solution:

CI = P [(1 + r/100)t - 1]

⇒ 1908 = P [(1 + 12/100)2 - 1]

⇒ 1908 = P [(1 + 3/25)2 - 1]

⇒ 1908 = P [(28/25)2 - 1]

⇒ 1908 = P [784/625 - 1]

⇒ 1908 = P × 159 / 625

⇒ P = 1908 × 625 / 159

⇒ P = 12 × 625 = Rs. 7500

Hence, the principal is Rs. 7,500.

The simple interest on a certain principal amount for 4 years at 10% per annum is half of the compound interest on Rs. 1000 for 2 years at 20% per annum. Find the principal amount 

  1. Rs. 500
  2. Rs. 450
  3. Rs. 650
  4. Rs. 550

Answer (Detailed Solution Below)

Option 4 : Rs. 550

Simple and Compound Both Question 8 Detailed Solution

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Calculation:

The effective rate of 20% for 2years is = 20 + 20 + (20 × 20)/100 = 44%

So, C.I on 1000 for 2 years is = 1000 × 44/100 = 440

Let the principal invest in S.I be P

Now, according to the question,

(P × 4 × 10)/100 = 440/2

⇒ P = 1100/2 = 550

∴  The principal amount be 550 

The difference between the simple interest and compound interest (interest is compounded half yearly) on a sum at the rate of 25% per annum for one year is ₹ 4375. What will be the principal?

  1. ₹ 280000
  2. ₹ 85000
  3. ₹ 80000
  4. ₹ 75000

Answer (Detailed Solution Below)

Option 1 : ₹ 280000

Simple and Compound Both Question 9 Detailed Solution

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Given:

The difference between the simple interest and compound interest (interest is compounded half yearly) on a sum at the rate of 25% per annum for one year is ₹ 4375

Formula used:

Simple Interest = (P × N × R)/100

Compound Interest = [P(1 + (r/200))T] - P      (for compounded half yearly)

Calculation:

Let P be the Principal,

S.I = (P × 1 × 25)/100 = P/4

C.I = [P(1 + (25/200))2] - P        ( T = 2   ∵ compounded half yearly for 1 year)

⇒ C.I = 17P/64

Now, C.I - S.I = (17P/64) - (P/4) = P/64

⇒ P/64 = 4375

∴ P = 64 × 4375 = 280000

Shortcut TrickFormula used:

CI - SI = P(R/100)2

Rate (R) = 25%/2 due to the compounded half-yearly.

⇒ 4375 = P (25/200)2

⇒ P = 4375 × 64

⇒ P = 280,000

∴ The sum is Rs. 280,000.

The simple interest on a certain sum of ₹ P at a rate of r% per annum for 3 years is Rs.11,250 and the compound interest on the same sum for 2 years at the same rate percent p.a. is ₹ 7,650. What is the value of P and r, respectively?

  1. ₹ 93750 and 4%
  2. ₹ 93750 and 5%
  3. ₹ 92500 and 6%
  4. ₹ 92500 and 7%

Answer (Detailed Solution Below)

Option 1 : ₹ 93750 and 4%

Simple and Compound Both Question 10 Detailed Solution

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Given data:

SI for 3 years = Rs 11,250

CI for 2 years at the same rate = Rs 7650

Formula used:

P = \(SI\times 100\over {R\times T}\) where-

P = Principal

SI = Simple Interest

R = Rate

T = Time

Calculation:

SI for 1 year = 11,250 ÷ 3 = Rs 3,750

SI for 2 year = 2 × 3750 = Rs 7500

Difference between CI and SI for 2 year = 7650 - 7500 = Rs 150

⇒ This difference between CI and SI was on the SI for the 1st year i.e., Rs 3750

∴ Rate % = \(150\over 3750\) × 100 = 4%

Principal = \(3750\times 100\over {1\times4}\) = Rs 93,750

The Principal amount was Rs 93,750 and the rate of interest was 4%. 

The difference between the compound interest and the simple interest accrued on an amount of ₹40,000 in 2 years was ₹324. The rate of interest per annum was:

  1. 7%
  2. 9%
  3. 12%
  4. 8%

Answer (Detailed Solution Below)

Option 2 : 9%

Simple and Compound Both Question 11 Detailed Solution

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Given:-

CI - SI = 324

Principal = 40000, Time = 2 years

Formula used:-

Compound Interest = Amount - Principal

CI = P[(1 + R/100)n - 1]

Simple interest = (P × R × T)/100

Calculation:-

According to question-

⇒ P[(1 + R/100)n - 1] - (P × R × T)/100 = 324

⇒  40000 [(1 + R/100)2 - 1] - (40000 × R × 2)/100 = 324

⇒ 40000 [{(100 + R)2/1002 - 1} - {R × 2}/100 = 324

⇒ 400 [{1002 + R2 + 2 × 100 × R -1002}/100 - 2R] = 324

⇒ [{R2 + 200R}/100 - 2R] = 324/400

⇒ (R2 + 200R - 200R)/100 = 324/400

⇒ R2 = 32400/400

⇒ R2 = 81 = 9%

 The rate of interest per annum is 9%.

Shortcut TrickFormula used:-

Difference between CI - SI for 2 years, 

⇒ D = P(R/100)2

Where,

D = Difference, P = Principal, R = Rate of interest

Calculation:-

⇒ 324 = 40000(R/100)2

⇒ R2 × 40000 = 3240000

⇒ R2 = 81

⇒ R = 9%

Required rate of interest is 9%.

If the simple interest for 2 years is Rs. 500 at 10% rate of interest. Find the compound interest for the same time.

  1. Rs. 525
  2. Rs. 500
  3. Rs. 200
  4. Rs. 210

Answer (Detailed Solution Below)

Option 1 : Rs. 525

Simple and Compound Both Question 12 Detailed Solution

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Given:

Time = 2 years, Simple Interest = 500, rate = 10%

Formula used:

Simple Interest = (Principal × Rate × Time)/100

Compound Interest = Principal[(1 + rate/100)t – 1]

Calculation:

Let the principal be ‘P’.

Simple Interest = (Principal × Rate × Time)/100

⇒ 500 = (Principal × 10 × 2)/100

⇒ Principal = 2500

Compound Interest = Principal[(1 + rate/100)t – 1]

⇒ 2500[(1 + 10/100)2 – 1]

⇒ 525

The compound Interest is Rs 525.

On a sum of money, the compound interest for 2 years is Rs. 832, while the simple interest for the same time period is Rs.800, then find out the difference amount for period of 3 years?

  1. 98.56
  2. 96.43
  3. 90
  4. None of these

Answer (Detailed Solution Below)

Option 1 : 98.56

Simple and Compound Both Question 13 Detailed Solution

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 1st

 2nd 

 

 SI

 400 

 400

 400

 CI 

 400

 432 

 432+432×8/100 

 

Rate = 32/400 × 100 = 8%

Total SI for 3 years = 1200

Total CI for 3 years = 1298.56

∴ Difference = 98.56

The difference in compound interest, under annual compounding, and simple interest on a certain sum at the same rate of interest in 2 years is 144% of the sum. Find the rate of interest per annum.

  1. 15%
  2. 100%
  3. 120%
  4. 20%

Answer (Detailed Solution Below)

Option 3 : 120%

Simple and Compound Both Question 14 Detailed Solution

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Given data:

The difference between Compound Interest (CI) and Simple Interest (SI) for 2 years = 144% of the principal (P)

Concept or formula:

Difference between CI and SI for 2 years is given by P × (r ÷ 100)2

Calculation:

Substitute the given values in the formula

⇒ 144% P = P × (r ÷ 100)2 

⇒ (144/100)P = P × (R/100)2

Taking square root on both sides,

⇒ 12/10 = R/100

⇒ R = 120

Hence, the rate of interest per annum is 120%.

What is the difference between the compound interest and the simple interest on a sum of Rs. 4500 for 3 years at the rate of 8% per annum?

  1. Rs. 87.70
  2. Rs. 87.50
  3. Rs. 85.70
  4. Rs. 88.70

Answer (Detailed Solution Below)

Option 4 : Rs. 88.70

Simple and Compound Both Question 15 Detailed Solution

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Here P = 4500 , T = 8 , R = 8%                                                   

Simple interest = (P × R × T)/100, where P is the principal, R is the rate of interest and T is the time period.

Compound interest = [P (1 + R/100)n] - P, where P is the principal, R is the rate of interest and n is the time period.

⇒ SI = (4500 × 8 × 3)/100 = Rs. 1080

⇒ CI = [4500 (1 + 8/100)3] - 4500 = Rs. 5668.7 - 4500 = 1168.7

∴ Required difference = Rs. 88.70

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