Question

On what Principal, compound interest compounded half-yearly is Rs. 1050 at the rate of 20% per annum for 1 year?
1. 6000
2. 5500
3. 5000
4. 4500

Answer 1

Correct Answer - Option 3 : 5000

Given:

Compound interest is Rs. 1,050

Rate of interest is 20%,

Compounded half-yearly for 1 year

Formula Used:

A = CI + P

A = P (1 + R/100)ⁿ,

where,

CI is compound interest

A is amount,

P is  principle, 

R is rate of interest,

n is total number of years

Calculation:

Compounded half-yearly,

⇒ Time = 2 × of a year

⇒ Time = 2

Rate of interest when compounded half-yearly,

⇒ R = 1/2 of actual R 

⇒ R = 1/2 × 20

⇒ R = 10%

Let the principle b Rs. x,

Now using the formula and putting the value,

⇒ A = x (1 + R/100)ⁿ

⇒ x + 1,050 = x (1 + 10/100)²

⇒ x + 1,050 = x (11/10)²

⇒ x + 1,050 = x(121/100)

⇒ 1,050 = (121/100)x – x

⇒ 1,050 = 21/100 x

⇒ x = (1,050 × 100)/21

⇒ x = 5,000

∴ The principle is Rs. 5,000.