Quantity B: The simple interest on a certain amount for 5 years at 4%

1.	Quantity B: The simple interest on a certain amount for 5 years at 4% per annum is 1/4th of compound interest on Rs. 5500 for a year at 10%per annum. The difference between sum placed in Compound interest and sum placed in Simple interest is –1). Quantity A > Quantity B2). Quantity A < Quantity B3). Quantity A ≥ Quantity B4). Quantity A ≤ Quantity B
Answer» QUANTITY A: PRINCIPAL = 6000 Principal amount BECOMES double after 4 YEARS then, Using Compound interest formula, Let P = principal, R = rate of interest and N = time period Amount = P(1 + R/100)^N 12000 = 6000(1 + R/100)⁴ 2 = (1 + R/100)⁴ After 16 years it will becomes, (1 + R/100)¹⁶ = ? [(1 + R/100)⁴]⁴ = 2⁴ 2⁴ = 16 In 16 years it will becomes 16 times = 6000 x 16 = 96000 Quantity B: Let Principal amount for SI be Rs.a. Simple interest = (a × 5 × 4)/100 = a/5 Compound interest calculated annually, Compound interest = P(1 + R/100)^N – P Compound interest = 5500(1 + 10/100) – 5500 Compound interest = 5500 × 1.1 – 5500 = 550 Given, Simple interest = (1/4) × Compound interest Simple interest = 550/4 Simple interest = 137.5 Simple interest = a/5 = 137.5 a = 687.5 Difference between the sum placed in Compound interest and simple interest = = 5500 – 687.5 = 4812.5 From above SOLUTION, Quantity A > Quantity B

Quantity B: The simple interest on a certain amount for 5 years at 4% per annum is 1/4th of compound interest on Rs. 5500 for a year at 10%per annum. The difference between sum placed in Compound interest and sum placed in Simple interest is –1). Quantity A > Quantity B2). Quantity A < Quantity B3). Quantity A ≥ Quantity B4). Quantity A ≤ Quantity B

Answer»

Principal amount BECOMES double after 4 YEARS then,

Using Compound interest formula,

Let P = principal, R = rate of interest and N = time period

Amount = P(1 + R/100)^N

12000 = 6000(1 + R/100)⁴

2 = (1 + R/100)⁴

After 16 years it will becomes,

(1 + R/100)¹⁶ = ?

[(1 + R/100)⁴]⁴ = 2⁴

2⁴ = 16

In 16 years it will becomes 16 times = 6000 x 16 = 96000

Quantity B:

Let Principal amount for SI be Rs.a.

Simple interest = (a × 5 × 4)/100 = a/5

Compound interest calculated annually,

Compound interest = P(1 + R/100)^N – P

Compound interest = 5500(1 + 10/100) – 5500

Compound interest = 5500 × 1.1 – 5500 = 550

Given,

Simple interest = (1/4) × Compound interest

Simple interest = 550/4

Simple interest = 137.5

Simple interest = a/5 = 137.5

a = 687.5

Difference between the sum placed in Compound interest and simple interest =

= 5500 – 687.5

= 4812.5

From above SOLUTION,

Quantity A > Quantity B