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

Given:

Principal (P) = ₹9800

Rate of interest (R) = 78% per annum

Time (T) = 27 years

Formula used:

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

Calculation:

SI = (9800 × 78 × 27) / 100

SI = (9800 × 2106) / 100

SI = 20638800 / 100

SI = ₹206388

∴ The simple interest earned on the investment is: ₹206388

Given:

Principal (P) = ₹100

Rate of interest (R) = 10%

Time (T) = 1 year

Formula used:

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

Calculation:

SI = (100 × 10 × 1) / 100

SI = 1000 / 100

SI = ₹10

∴ The simple interest is: ₹10

Given:

Down payment = Rs. 10,000

Two equal annual installments = Rs. 12,100 each

Interest rate = 10% per annum, compounded yearly

Calculation:

Present value (PV) of the first installment (due after 1 year):

⇒ PV = 12100 ÷ (1 + 10/100) = 12100 ÷ 1.10 = Rs. 11000

Present value (PV) of the second installment (due after 2 years):

⇒ PV = 12100 ÷ (1.10 × 1.10) = 12100 ÷ 1.21 = Rs. 10000

Total cash value of the motorcycle:

⇒ Cash value = Down payment + PV of 1st installment + PV of 2nd installment

⇒ Cash value = 10000 + 11000 + 10000 = Rs. 31,000

Thus, the correct answer is Rs. 31,000.

Given

Rs. 72 amounts to Rs. 104.4 in 3 years

Formula used:

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

Calculation

Interest = Amount - Principal

Interest = 104.4 - 72 = 32.4

⇒ 32.4 = (72 x Rate x 3) / 100

⇒ Rate = (100 × 32.4) / (72 x 3) 

⇒ Rate = 3240 / 216

⇒ Rate = 15%

Now,

Simple Interest = (120 x 15 x 5) / 100

Simple Interest = 9000 / 100

Simple Interest = 90

Amount = 120 + 90

Amount = 210

The amount will be 210.

Shortcut TrickSince the rate is the same in both cases, we can use the ratio method, by calculation interest for the same number of years.

3 year interest = 104.4 - 72 = 32.4

1 year interest = 32.4/3 = 10.8

5 year interest = 10.8 × 5 = 54

Let the amount on the sum of 120 be a.

⇒ (72 + 54)/72 = a/120

⇒ 7/4 = a/120

⇒ a = 210

Given:

Sum of Rs.15,625 is invested for 3 years at 4% per annum

Formula Used:

S.I. = $\frac{(P\times R\times T)}{100}$ 

A = P × (1 + $\frac{R}{100}$)^t 

A = P  + C.I. 

Where, S.I. = Simple Interest, P = Principal , T = Time in years

R = Rate of interest, A = Amount 

Calculation:

Here, we have Principal = Rs.15625, t = 3 years, r = 4%

S.I. = $\frac{(15625\times 3\times 4)}{100}$ = Rs.1875 

Now, we have

A = P × (1 + $\frac{R}{100}$)^t

⇒ A = 15625 × (1 + $\frac{4}{100}$)³  = 15625 × $\frac{26}{25}$ × $\frac{26}{25}$ × $\frac{26}{25}$ 

⇒ A = Rs.17576 

Now, C.I. = A - P 

⇒ C.I. = 17576 - 15625 = Rs.1951 

Now, difference between compound interest and simple interest = Rs(1951 - 1875) = Rs.76 

Hence, the required difference is Rs.76.

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,

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

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

$\Rightarrow 3^3=(1+\frac{R}{100}{)}^3$

$\Rightarrow 3=(1+\frac{R}{100})$

⇒ 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.