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

Calculation

A:

SI = 6000

Principal = 8000

Time = 3 years
SI = [P × R × T]/100

So, 6000 = [8000 × R × 3/ 100]

⇒ R = 600000 / 24000 = 25

So, R = 25%

B:

CI = 2816

P = 6400, T = 2 years
Use formula:
CI = P [(1 + r/100) ² − 1]

So, 2816 = 6400[(1 + r/100)2 − 1]

⇒ [ 2816/6400] = (1+r/100)2 −1

⇒ 0.44 = (1 + r/100)2 – 1

⇒ (1 + r/100)2 = 1.44

⇒ [1 + r/100] = 1.2

⇒ r = 20

So, R = 25, r = 20
Required ratio:

So, [R + r] :[R − r] = (25 + 20):(25 − 20) = 45:5 =9:1

Given:

Principal (P) = ₹17,700

Rate of Interest (r) = 4% per annum

Time (t) = 2 years

Formula used:

Simple Interest (SI) = (P × r × t) / 100

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

Difference between CI and SI = CI - SI

Calculations:

Simple Interest (SI):

SI = (17700 × 4 × 2) / 100

⇒ SI = (141600) / 100

⇒ SI = ₹1,416

Compound Interest (CI):

CI = 17700 × (1 + 4/100)² - 17700

⇒ CI = 17700 × (1.04)² - 17700

⇒ CI = 17700 × 1.0816 - 17700

⇒ CI = 19144.32 - 17700

⇒ CI = ₹1,444.32

Difference between CI and SI:

Difference = CI - SI

⇒ Difference = 1444.32 - 1416

⇒ Difference = ₹28.32

∴ The correct answer is option (3).

Shortcut Trick

Given:

Principal (P) = ₹47,100

Rate (R) = 9%

Time = 2 years

Formula used:

Difference for 2 years = P

Calculations:

⇒

⇒

⇒ Difference = 47100 × 0.0081 = 381.51

∴ The difference between CI and SI for 2 years = ₹381.51.

Alternate Method

Formula used:

Simple interest (SI) =

Compound interest (CI) = P

Calculations:

SI = = = 8478

CI = 47100 = 47100

1.09² = 1.1881 ⇒ CI = 47100 = 8859.51

Difference = CI – SI = 8859.51 – 8478 = 381.51

∴ The difference between compound and simple interest = ₹381.51.

Given:

Rate (r) = 16% per annum

Time (t) = 2 years

Difference between CI and SI = ₹797

Formula used:

Difference (CI − SI) for 2 years =

Calculation:

⇒

⇒

⇒

∴ The correct answer is (rounded to nearest integer).

Calculation

Given:

Difference between 3rd and 2nd year SI = x – 3000

So, x – 3000 = 0 [ because SI is same all over the year]

So, x = 3000

SI = (2x + 4000) × R × 3 / 100 = 6000

→ (6000 + 4000) × R = 200000

→ R = 200000 / 10000

R = 20%

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.

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 

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.

Given data:

SI for 3 years = Rs 11,250

CI for 2 years at the same rate = Rs 7650

Formula used:

P =  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 % =  × 100 = 4%

Principal =  = Rs 93,750

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

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%.

Rate = 32/400 × 100 = 8%

Total SI for 3 years = 1200

Total CI for 3 years = 1298.56

∴ Difference = 98.56

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.

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%.

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