If the amount is Rs 400 and the principal is Rs 100 compounded half yearly for 1 year, calculate the interest rate.

Formula Used:
A = P (1+ (r/100))^T

Where:

A = amount after interest,

P = principal amount,

R = annual interest rate (in decimal form),

T = time the money is invested or borrowed for years.

Calculation:

According to the question,

The principal amount Rs. 100 is invested compounded half yearly,

so, Rate will become half and Time will become twice.

New Rate of interest = r/2

New Time = 2 x 1 = 2 years

⇒ 400 = 100 (1+ (r/2)/100))²

⇒ 4 = (1+ (r/2)/100))²

⇒ 2 = 1+ [(r/2)/100]

⇒ 1 = r/200

⇒ r = 200 %

 ∴ The correct answer is 200%.