Interest MCQ Quiz - Objective Question with Answer for Interest - Download Free PDF

Given

Loan amount = ₹9,960

Interest rate = 7.5% per annum compounded annually

Repayment period = 2 years

Shortcut Trick 

Rate of interest = 7.5%

If Principal = 100

Amount = 107.5

So

Principal : Amount = 100 : 107.5 = 40 : 43

So  

                    Principal      Installment

First year          40               43

Second year     40²             43²

Both installments are equal so

                       Principal      Installment 

First year        40 × 43        43 × 43      

Second year     402               432

So

Total Principal = 40 × 43 + 40² = 3320

3320 units = Rs. 9960

1 unit = 3

so

Installment = 43² × 3 = Rs. 5547

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

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

Given:

Principal (P) = ₹1200

Amount (A) = ₹1440

Time (t) = 2 years

Formula Used:

Simple Interest (SI) = A - P

SI = \(\dfrac{P \times r \times t}{100}\)

Where, r = rate of interest

Calculations:

SI = \(\dfrac{P \times r \times t}{100}\):

240 = \(\dfrac{1200 \times r \times 2}{100}\)

⇒ 240 = 12 × r × 2

⇒ 240 = 24 × r

⇒ r = \(\dfrac{240}{24}\)

⇒ r = 10%

∴ The rate of interest is 10% per annum.

Given:

Simple Interest (SI) = ₹420

Annual Rate of Interest (R) = 10%

Time (T) = 2 years

Formula Used:

Simple Interest (SI) = (Principal (P) × Rate (R) × Time (T)) / 100

To find the Principal (P), rearrange the formula: P = (SI × 100) / (R × T)

Calculation:

P = (420 × 100) / (10 × 2)

P = 42000 / 20

P = 2100

∴ The principal amount is ₹2100.

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%

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.

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%.

Given: 

Amount produce in 7 years = Rs.14522

Amount produce in 11 years = Rs.18906

Formula used:

Simple interest (S.I) = (P × R × T)/100

Calculation:

Amount produce in 7 years = Rs.14522

Amount produce in 11 years = Rs.18906

S.I produced in (11 - 7) = 4 years = (18906 - 14522) = Rs.4384

S.I in 1 years = 4384/4 = 1096

Principal = 14522 - (1096 × 7)

⇒ (14522 - 7672) = Rs.6850

∴ The correct answer is Rs.6850.

Concept Used:

In this type of question, number can be calculated by using the below formulae

Formula Used:

If a sum with simple interest rate, amounts to Rs. ‘A’ in y years. and Rs. ‘B’ in z years. then,

P = (A × z – B × y)/(z – y)

Calculation:

Using the above formulae, we have

⇒ P = (10650 × 6 – 11076 × 5)

⇒ P = Rs. 8520

∴ Required principal is Rs. 8520 

A sum becomes Rs. 10650 in 5 years. and Rs. 11076 in 6 years. at simple interest

Interest of 1 year = 11076 – 10650 = Rs. 426

Interest of 5 year = 426 × 5 = 2130

∴ Required principal = 10650 – 2130 = Rs. 8520

Given:

Principal = Rs. 8000

Rate = 10%

Time =  \(2\frac{2}{5}\) years

Formula used:

SI = (P × t × r)/100

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

P = Principal

t = time

r = rate

Calculation:

SI = (8000 × 12 × 10)/(100 × 5)

⇒ Rs. 1920

CI = 8000[1 + 10/100]² × [1 + 4/100] - 8000

⇒ 8000 × 11/10 × 11/10 × 26/25 - 8000

⇒ 10067.2 - 8000

⇒ 2067.2

Difference = 2067.2 - 1920 = 147.2

∴ Required difference is Rs. 147.2

Shortcut Trick 

So, the difference of CI and SI = 80 + 32 + 32 + 3.2

∴ The Difference of CI and SI = 147.2.

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 of Principal 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.

Given:

Amount = 2P

Time = 10 years

Formula used:

SI = (PRT/100) 

Amount = (PRT/100) + P

Calculation:

Amount = (PRT/100) + P

2P = (PR/10) + P 

⇒ P = (PR/10) 

⇒ R = 10%

According to the question, Amount = 3P

3P = (10PT/100) + P 

⇒ 2P = (PT/10)

⇒ T = 20 years

 ∴ Time taken to triple the amount is 20 years.

Shortcut TrickInterest = 2P - P = P = 100% of principle

Time = 10 year

Hence, rate = Interest/Time = 100/10 = 10%

New interest = 3P - P = 2P = 200% of principle

∴ Time = Interest/Rate = 200/10 = 20 Years

Interest earned for 5 years – Interest earned for 4 years = 375

Let the principal be Rs. P,

⇒ (P × 7.5 × 5) /100 – (P × 7.5 × 4) /100 = 375

⇒ (37.5 × P) /100 – (30 × P) /100 = 375

⇒ (7.5 × P) /100 = 375

Given:

Amount after 3 years = Rs. 715

Amount after 8 years  = Rs. 990

Formula used:

A = P + SI

Where A = amount , P = Principle

And SI = Simple interest

Calculation:

Amount in 3 years = Rs. 715

Now it is given in the question, amount for the time of further 5 years i.e 

Total time = 5 years + 3 years = 8 years.

Amount in 8 years = Rs. 990

SI for 5 years = Amount after 8 years  - Amount after 3 years

⇒ SI for 5 years = 990 - 715 = 275

SI for 1 years = 275/5 = 55

SI for 3 years = 55 × 3 = Rs.165

P = Amount of 3 years - SI of 3 years

⇒ P = 715 - 165 = 550

∴  The sum is Rs. 550

Confusion Points It is given in the question that after further 5 years amount is calculated , so total time will be (5 +3) years = 8 years. not 5 years.