A bank gives 12% per annum interest on an account. If the interest is compounded half-yearly, then _______ of the principal would have been earned more in a year as interest on the account.

Correct option is A

Given:

Annual interest rate = 12%

Compounded half-yearly

Time = 1 year

Formula Used:

Compound Amount for half-yearly compounding:

A = $$P \left(1 + \frac{R/2}{100} \right)^{2}$$​​

Compound Interest (CI) = A − P

Simple Interest (SI) = $$\frac{P \times R \times T}{100}$$​​

Difference = CI − SI

Solution:

Let Principal P = 100

Half-yearly rate = $$\frac{12}{2} = 6\%$$​​

Compounded twice:

A = $$100 \left(1 + \frac{6}{100} \right)^2$$​​

​$$= 100 \times (1.06)^2$$​​

​$$= 100 \times 1.1236$$​​

= 112.36

CI = 112.36 - 100 = 12.36

Now, 

SI = $$100 \times \frac{12}{100} = 12$$​​

Extra Interest = 12.36 - 12 = 0.36

Thus, 0.36% more would be earned in a year.