The rate of interest is 8% per annum and the interest is compounded semi-annually. The equivalent rate of interest per annum in a time period of one year is ____%.

Correct option is B

Given:

Rate of Interest (r) = 8% per annum

Compounding frequency = Semi-annually (2 times a year)

Formula used:

Equivalent rate $$=\left( 1 + \frac{r}{n} \right)^n - 1$$​​

Where, n = number of times interest is compounded in a year.

Solution:

Here,

n = 2

r = Annual interest rate ( as a decimal ) = 8% = 0.08

Equivalent rate = $$\left( 1 + \frac{0.08}{2} \right)^2 - 1$$​​​

Equivalent rate =$$\left( 1 + 0.04 \right)^2 - 1$$​ 

Equivalent rate =$$(1.04)^2 - 1$$

Equivalent rate = $$(1.0816 - 1)$$

Equivalent rate = 0$$.0816$$​

Equivalent rate = 8.16%