[Solved] Compound Interest MCQ [Free PDF] - Objective Question Answer for Compound Interest Quiz - Download Now! (2024)

1. Rs.1600
2. Rs.1640
3. Rs.1700
4. More than one of the above
5. None of the above

Concept -

The formula to calculate compound interest compounded half-yearly is:

\( A = P \times \left(1 + \frac{r}{n}\right)^{n \times t} \)

Where:
Ais the amount after t" id="MathJax-Element-3-Frame" role="presentation" style="position: relative;" tabindex="0">tt" id="MathJax-Element-72-Frame" role="presentation" style="position: relative;" tabindex="0">t$t$ years.
Pis the principal amount (initial amount).
r is the annual interest rate.
n is the number of times the interest is compounded per year.
t is the time the money is invested for in years.

Explanation :
Principal amount P = Rs. 16000
Annual interest rater = 10% per annum
Time t = 1 year
Interest is compounded semi-annually, so n = 2 (twice a year)

Let's plug the values into the formula to find the compound interest:

\( A = 16000 \times \left(1 + \frac{10}{2 \times 100}\right)^{2 \times 1}\)

\( A = 16000 \times \left(1 + \frac{0.10}{2}\right)^2\)
\(A = 16000 \times \left(1 + 0.05\right)^2\)
\( A = 16000 \times (1.05)^2 \)
A ≈ 17640

The amount after one year with compound interest is approximately Rs. 17640.

Now, to find the compound interest:

Compound Interest = Amount after tyears - Principal Amount
Compound Interest = 17640 - 16000
Compound Interest = 1640

Therefore, the compound interest on Rs. 16000 at 10% per annum for 1 year, compounded semi-annually, is Rs. 1640.

Hence option(2) is correct.

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1. 1760
2. 1756.4
3. 1846.4
4. More than one of the above
5. None of the above

Given:

Principal = Rs. 4000, Time = 2 years, Rate = 20%

Formula used:

A = P(1 + r/100)n

Calculation:

A = P(1 + r/100)n

⇒ A = 4000[(1 + 20/100)2

⇒A = 4000 × (6/5)× (6/5)

⇒A = 5760

CI = 5760 - 4000 = 1760

∴ The answer is 1760.

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1. Rs.2200
2. Rs. 3000
3. Rs.4400
4. More than one of the above
5. None of the above

Given:

Principal = Rs. 5000

The rate of interest = 20% per annum

Time = 2 years

Formula Used:

C.I = P[{1 + (R/100)}T- 1]

Where,

C.I = Compound Interest

P = Principal

R = Rate of Interest

T = Time

Calculation:

According to the question, we have

C.I = 5000[{1 + (20/100)}2- 1]

⇒ 5000[{1 + (1/5)}2- 1]

⇒ 5000[(6/5)2- 1]

⇒ 5000× [(36/25) - 1]

⇒ 5000× (36 - 25)/25

⇒ 200× 11

∴ The compound interest is Rs. 2200.

Shortcut Trick

Concept Used:

Total rate%of 2 years (at C.I) = [X+ X+ (X)2/100]%

Calculation:

Total rate%of 2 years = [20 + 20 + (20)2/100]%

⇒ [40+ 400/100]%

⇒ [40 + 4]%

⇒ 44%

According to the question, we have

C.I = 5000× (44/100)

⇒ 50× 44

⇒ 2200

∴ The compound interest is Rs. 2200.

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1. Rs.5606
2. Rs.600
3. Rs.606
4. More than one of the above
5. None of the above

Given:

Principal =Rs. 15,000 , time =1 year, rate% =4% per annum

Interest is compounded half yearly

Concept used:

When interest is compounded half yearly,half yearly rate = rate%/2andhalf yearly time = 2× time

For CI, Amount = Principal(1 + rate/100)^time, where CI = Amount- Principal

Calculation:

Now,half yearly rate = rate%/2 = 4/2 = 2%

andhalf yearly time = 2× time = 2× 1 = 2 years

Putting values, we get, Amount = 15000× (1 + 2/100)²

= 15000×(51/50)²

= 15000× 2601/2500

= 6× 2601

= 15606

∴CI = Amount- Principal = Rs. 15606 - Rs. 15000

= Rs. 606

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1. 741.81
2. 898.91
3. 841.81
4. More than one of the above
5. None of the above

Given:

Principal = Rs. 8000

Time = 9 Months

Rate of interest = 12% p.a.

Formula Used:

Compound interest = Principal×(1 + Rate%/100)^Time- Principal

Calculation:

Interest is compounded quarterly, So

Time = 9/3 = 3

Rate of interest = 12%/4= 3% p.a.

Compound interest = Principal×(1 + Rate%/100)Time- Principal

⇒ Compound interest = 8000×(1 + 3/100)3- 8000

⇒ Compound interest = 8741.81- 8000

⇒ Compound interest = Rs. 741.81

∴Compound interest is Rs. 741.81

The correct option is 1 i.e.Rs. 741.81

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Compound Interest Question 6

1. 150%
2. 100%
3. 300%
4. 200%

Compound Interest Question 6 Detailed Solution

Gi​ven:

Amount = 27 P in 3 years

Concept:

In compound interest, the ratio of the amount and the principal is given by:

\(\frac{A}{P} = (1 + \frac{R}{100})^n\)

Calculation:

We know that,

\(\frac{A}{P} = (1 + \frac{R}{100})^n\)

\(⇒ \frac{27}{1} = (1 + \frac{R}{100})^3 \)

\(⇒ 3^3 = (1 + \frac{R}{100})^3 \)

\(⇒ 3 = (1 + \frac{R}{100}) \)

⇒ R/100 = 3 - 1 = 2

⇒ R = 200%

Hence, the annual interest rate is 200%.

Shortcut Trick

A sum becomes 27 times in 3 years

3^x= 27

⇒ 3^x= 3³

⇒ x = 3

Rate = (x - 1)× 100%

⇒ (3 - 1)× 100% = 200%

∴ The annual interest rate is 200%.

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Compound Interest Question 7

1. 20%
2. 24%
3. 30%
4. 16%

Compound Interest Question 7 Detailed Solution

Given:

Principal = Rs. 15,000

Amount = Rs. 19,965

Time = 15 months

Condition = on every 5 months

Concept used:

Condition = on every 5 months

New rate = Rate × 5/12

New time = Time × 12/5

Calculations:

Let the new rate be R%

According to the question,

New time = Time × 12/5

⇒ 15 × 12/5 = 36 months = 3 years

Simplifying the values by dividing it by 15 to its lowest possible values, we get Principal = 1000 and Amount = 1331

Now, new time period is 3 years, hence taking the cube roots ofPrincipal and Amount,

⇒ R = 10%

New rate = Rate × 5/12

⇒ 10 = Rate × 5/12

⇒ Rate = (10 × 12)/5

⇒ Rate = 24%

∴ Rate is 24% per annum.

Alternate MethodGiven:

Principal = Rs. 15,000

Amount = Rs. 19,965

Time = 15 months

Condition = on every 5 months

Concept used:

Condition = on every 5 months

New rate = Rate × 5/12

New time = Time × 12/5

Formulae used:

(1) Effective rate for 3 years = 3R + 3R²/100 + R³/10000

(2) A = P(1 + R/100)^T

Where, A → Amount

P → Principal

R → Rate of interest

T → Time

Calculations:

According to the question,

Let the new rate be R%

New time = Time × 12/5

⇒ 15 × 12/5 = 36 months = 3 years

Amount = P(1 + R/100)^T

⇒ 19,965 = 15,000(1 + R/100)³

⇒ 19,965/15,000 = (1 + R/100)³

⇒ 1331/1000 = (1 + R/100)³

⇒ (11/10)³ = (1 + R/100)³

⇒ 11/10 = 1 + R/100

⇒ (11/10) – 1 = R/100

⇒ 1/10 = R/100

⇒ R = 10%

New rate = Rate × 5/12

⇒ 10 = Rate × 5/12

⇒ Rate = (10 × 12)/5

⇒ Rate = 24%

∴ Rate is 24% per annum

Additional InformationCompound Interest means interest earned on interest. Simple interest always occurs on only principal but compound interest also occurs on simple interest. So, if time period is 2 years, compound interest will also apply on simple interest of first year.

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Compound Interest Question 8

1. Rs. 4,404
2. Rs. 4,330
3. Rs. 4,033
4. Rs. 4,303

Compound Interest Question 8 Detailed Solution

Given:

Principal = Rs.13000

Rate of interest = 15%

Concept used:

Rate of interest for 12 months = 15%

Rate of interest for 8 months= 15 × (8/12) = 10%

And 2 years = 24 months

Total8-monthly time = 24/8 = 3

Formula:

Let P = Principal, R = rate of interest and n= time period

Compound interest = P(1 + R/100)ⁿ- P

Calculation:

∴ Compound interest = 13000(1 + 10/100)³ - 13000

⇒ 13000× (1331/1000)

⇒ 17303 -13000

= Rs.4303

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Compound Interest Question 9

1. 2 years
2. 3 years
3. 1.5 years
4. 2.5 years

Compound Interest Question 9 Detailed Solution

Given:

Principal = Rs. 60,000

Rate = 9%

Compound Interest = Rs. 11,286

Amount = Principal + Compound Interest

Formula used:

Amount = P(1 + Rate/100)^Time

Amount =Principal + Compound Interest

Calculation:

Amount = 60,000 + 11,286 = 71,286

Amount = P(1 + Rate/100)Time

⇒ 71,286 = 60,000(1 + 9/100)^Time

⇒ 71,286 = 60,000[(100 + 9)/100]^Time

⇒ 71,286/60,000 = (109/100)^Time

⇒ (11,881/10,000) = (109/100)^Time

⇒(109/100)2= (109/100)Time

⇒ Time = 2

∴ The time period is 2 years.

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Compound Interest Question 10

1. 20%
2. 26%
3. 18%
4. 15%

Compound Interest Question 10 Detailed Solution

Given:

The Sumbecomes Rs. 7800 in 3 years and Rs. 11232 in 5 years

Formula used:

Atcompound interest, the final amount=\(P\left(1+\frac{r}{100} \right)^{n}\)

Where, P = The sum of the amount

r = Rate of interest

n = Time (years)

Calculation:

Here, Rs. 7800becomes Rs. 11232at compound interest in twoyears.

Let, the rate of interest = R

So, 11232=\(7800\left(1+\frac{R}{100} \right)^2\)

⇒ [(100 + R)/100]² = 11232/7800

⇒ [(100 + R)/100]2=144/100

⇒ [(100 + R)/100]2=(12/10)²

⇒ [(100 + R)/100]=(12/10)

⇒100 + R = 1200/10 = 120

⇒R = 120 - 100 = 20

∴ The rate per cent is 20%

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Compound Interest Question 11

1. 8,500
2. 7,800
3. 8,000
4. 7,500

Compound Interest Question 11 Detailed Solution

Given:

Amount = Rs. 9982.5

Rate = 12%

Time =\(2\frac{1}{2}\)years

Concept used:

A = P(1 + r/100)^t

Here,

A = amount, P = principal or sum, r = rate, t = time

When interest is calculated on a certain monthly

Then,

r = (r/12)× month

t = total month given in the form of year/no. of months

Calculation:

\(2\frac{1}{2}\)years = 30 months [As 1 year = 12 months]

So, t= 30/10 = 3

r = (12/12)× 10 = 10%

Let the sum be Rs. P

Now,

9982.5 = P(1 + 10/100)³

⇒9982.5 = P(1 + 1/10)3

⇒9982.5 = P(11/10)3

⇒9982.5 = 1331P/1000

⇒ P = 9982.5× (1000/1331)

⇒ P = 7500

So, sum = Rs. 7500

∴The sum (in Rs.) is Rs 7500.

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Compound Interest Question 12

1. 8
2. 9
3. 6
4. 12

Compound Interest Question 12 Detailed Solution

GIVEN:

A sum of money when invested at compound interest for 3 years becomes 4 times.

CONCEPT:

Compound interest concept.

FORMULA USED:

Amount = P × (1 + R/100)^T

Where, P →Principal, R →Rate, T →Time

CALCULATION:

Suppose Principal = Rs. P

⇒ Amount after 3 years = 4P

According to the question,

4P = P × (1 + R/100)³

⇒ (1 + R/100)³ = 4 ----(i)

Now,

A = 16P, Time = T (Suppose)

⇒ 16P = P × (1 + R/100)^T

⇒ (1 + R/100)^T = 16 = 4²

From equation (i):

(1 + R/100)^T = (1 + R/100)⁶

⇒ T = 6

∴ The sum will be 16 times in 6 years.

In case of Compound interest:

If a sum becomes ‘x’ times in ‘t’ years:

It will be ‘x²’ times in ‘2t’ years.

It will be ‘x³’ times in ‘3t’ years and so on.

∴ When a sum of money when invested at compound interest for 3 years becomes 4 times, it will be 16 ( = 4²) times in 6 ( = 2 × 3) years.

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Compound Interest Question 13

1. 1740
2. 1735
3. 1634
4. 1640

Compound Interest Question 13 Detailed Solution

Given:

Principal = Rs.8192

Time =\(1 \frac{1}{4}\)years or 15 months

Rate = 15% Per annum

⇒ Rate as per 5-monthly basis = 5/12× 15 = 25/4%

Formulas used:

Compound Interest = Amount - Principal

Amount = P× (1 + R/100)ⁿ

Calculation:

Time period = 3 (15 months/5)

Rateas per 5-monthly basis = 5/12× 15 = 25/4%

Compound Interest = 8192× (1 + 25/4÷100)³- Principal

⇒ 8192× (1 + 1/16)³- 8192 = 8192 [ 17/16× 17/16× 17/16 - 1]

⇒ 8192 [(4913 - 4096)÷ 4096]

⇒ 8192× 817/4096

⇒ 1634

∴ Compound Interest = Rs.1634

Alternate MethodBy Fraction Method

Rate = 25/4% = 25/4× 100 = 1/16

CI is calculated on Principal, so it will be the base (100%) for the interest.

Rate % = Rate/100 = Interest/Principal

⇒ Interest/Principal = 1/16

Interest = Amount -Principal

⇒ Amount = 1 + 16 = 17

Time Period = 3 (5-monthly)

\(=\frac{Principal}{Amount}=\left(\frac{16}{17}\right)^{n}=\frac{16^3}{17^3}\)

⇒ 8192/ Amount = 4096/4913

⇒ So, if 4096 = 8192,

So, Compound Interest (4913 - 4096) = 817;

⇒ 817 = 817/4096× 8192 = 1634

∴ Compound Interest = Rs.1634

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Compound Interest Question 14

1. ₹2,500
2. ₹1,800
3. ₹3,800
4. ₹2,200

Compound Interest Question 14 Detailed Solution

GIVEN:

Amount at the end of 2 years = Rs 3,364

Rate = 16%.

FORMULA USED:

A = P×\(( 1+ \frac{R}{100})^t\)where, A = Amount, P = Principal,

R = Rate of interest and T= Time.

CALCULATION:

A = P×\((1 +\frac{R}{100})^t\)

⇒ 3,364 = P×\(( 1+ \frac{16}{100})^2\)

⇒ 3,364 = P×\(29\over25\)×\(29\over25\)

⇒ P =Rs 2500.

∴ The sum is Rs.2500.

Shortcut TrickR = 16% = 4/25

1st year 2nd year

25 29

25 29

29 × 29→ 3364,1→ 4

Sum→ 4 × 25 × 25 = 2500.

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Compound Interest Question 15

1. 5500
2. 4500
3. 5000
4. 4800

Compound Interest Question 15 Detailed Solution

Given:

Compound Interest = Rs. 1655

Rate = 20%

Time = 1.5 years

Concept used:

When the sum is compounded half-yearly, then the rate of interest becomeshalfand time becomes double.

Formula used:

C.I = P[(1 + R/100)T- 1]

Where,P = Principal, T= Time, C.I = Compound interest and R = rate of interest

Calculation:

Rate = 20%/2 = 10%

Time = 1.5 years = 1.5× 2 = 3 years

Now,

C.I = P[(1 + R/100)T- 1]

⇒ 1655 =P[(1 + 10/100)³- 1]

⇒ 1655 = P[11/10× 11/10× 11/10 - 1]

⇒ 1655 = P[(1331/1000) -1]

⇒ P = (1655× 1000)/331 = Rs. 5000

∴ The sum is Rs. 5000.

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