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

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

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.

Given:

Compound Interest (CI) = ₹2,448

Rate of Interest (r) = 4%

Time (t) = 2 years

Formula used:

For Compound Interest: \(\text{CI} = P[(1 + \frac{r}{100})^t - 1]\)

For Simple Interest: \(\text{SI} = \frac{P \cdot r \cdot t}{100}\)

Calculations:

Using CI formula: \(\text{CI} = P[(1 + \frac{r}{100})^t - 1]\)

⇒ ₹2,448 = P[(1 + \(\frac{4}{100}\))² - 1

⇒ ₹2,448 = P[(1.04)² - 1]

⇒ ₹2,448 = P[1.0816 - 1]

⇒ ₹2,448 = P × 0.0816

⇒ P = \(\frac{2448}{0.0816}\)

⇒ P = ₹30,000

Now, using SI formula: \(\text{SI} = \frac{P \cdot r \cdot t}{100}\)

⇒ SI = \(\frac{30,000 \times 4 \times 2}{100}\)

⇒ SI = ₹2,400

∴ The correct answer is option (2).

Given:

Principal (P) = ₹10,000

Simple Interest (SI) = ₹2,400

Time (t) = 2 years

Formula used:

SI = \(\dfrac{P \times R \times T}{100}\)

CI = \(\dfrac{P \times (1+\frac{R}{100})^t - P}{1}\)

Calculation:

Calculate Rate (R) using Simple Interest formula:

2400 = \(\dfrac{10000 \times R \times 2}{100}\)

⇒ 2400 = \(\dfrac{20000 \times R}{100}\)

⇒ R = \(\dfrac{2400 \times 100}{20000}\)

⇒ R = 12%

 Calculate Compound Interest (CI):

CI = \(\dfrac{10000 \times (1+\frac{12}{100})^2 - 10000}{1}\)

⇒ CI = \(\dfrac{10000 \times (1+0.12)^2 - 10000}{1}\)

⇒ CI = \(\dfrac{10000 \times (1.12)^2 - 10000}{1}\)

⇒ CI = \(\dfrac{10000 \times 1.2544 - 10000}{1}\)

⇒ CI = \(\dfrac{12544 - 10000}{1}\)

⇒ CI = ₹2,544

∴ The correct answer is option (2).

Calculation

Let x be amount at 12%, then (6400 − x) at 20%

Interest for 2 years: ⇒ x × 12% × 2 + (6400 − x) × 20% × 2 = 2176
⇒ 0.24x + 0.4(6400 − x) = 2176
⇒ 0.24x + 2560 − 0.4x = 2176
⇒ -0.16x = -384
⇒ x = 2400

Rs. 2400 at 12%

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 = \(SI\times 100\over {R\times T}\) 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%. 

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%.

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%.

Rate = 32/400 × 100 = 8%

Total SI for 3 years = 1200

Total CI for 3 years = 1298.56

∴ Difference = 98.56

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