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

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

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:

Amount (A) = ₹ 9075

Time (T) = 1 and 1/3 years = 4/3 years

Rate of interest (R) = 15% p.a.

Compounded 8-monthly

Formula used:

For compound interest: A = P(1 + r/100)ⁿ, where:

A = Amount

P = Principal

r = Rate of interest per compounding period

n = Number of compounding periods

Calculation:

First, calculate the number of compounding periods (n) and the rate per compounding period (r).

Time in months = (4/3) years × 12 months/year = 16 months

Compounding period = 8 months

Number of compounding periods (n) = Total months / Compounding period = 16 / 8 = 2 periods

Annual rate = 15%

Rate per month = 15% / 12 = 5/4 %

Rate per 8-monthly period (r) = (5/4) % × 8 = 10%

Now, use the compound interest formula to find the Principal (P):

A = P(1 + r/100)ⁿ

9075 = P(1 + 10/100)²

9075 = P(1 + 1/10)²

9075 = P(11/10)²

9075 = P(121/100)

P = (9075 × 100) / 121

P = 75 × 100

P = ₹ 7500

SI on the same sum (P = ₹ 7500) for the same period (T = 4/3 years) and at the same rate (R = 15% p.a.).

SI = (P × R × T) / 100

SI = (7500 × 15 × (4/3)) / 100

SI = (7500 × 15 × 4) / (3 × 100)

SI = (75 × 15 × 4) / 3

SI = 25 × 15 × 4

SI = 25 × 60

SI = ₹ 1500

∴ The correct answer is option 3.

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:

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.

Rate = 32/400 × 100 = 8%

Total SI for 3 years = 1200

Total CI for 3 years = 1298.56

∴ Difference = 98.56

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