Question

The rate of interest at which the sum of money ₹ 2000 yields ₹ 420 as compound interest compounded annually in 2 years is ______.

Options

• 8%

• 10%

• 11%

• 12%

Answer 1

The rate of interest at which the sum of money ₹ 2000 yields ₹ 420 as compound interest compounded annually in 2 years is 10%.

Explanation:

The problem is to find the rate of interest (R%) at which ₹ 2000 yields ₹ 420 as compound interest compounded annually in 2 years.

Step 1: Identify given values:

• Principal (P) = ₹ 2000
• Compound Interest (C.I.) after 2 years = ₹ 420
• Time (T) = 2 years

Step 2: Calculate the amount (A) after 2 years:

Since C.I. = A – P, 

A = P + C.I. 

A = 2000 + 420 

A = ₹ 2420

Step 3: Use the compound interest formula:

`A = P xx (1 + R/100)^T`

Substituting the values:

`2420 = 2000 xx (1 + R/100)^2`

Divide both sides by 2000:

`1.21 = (1 + R/100)^2`

Take the square root on both sides:

`sqrt(1.21) = 1 + R/100`

`1.1 = 1 + R/100`

Solve for R:

`R/100 = 0.1`

R = 10