If 10 percent per annum rate of compound interest compounded yearly is equivalent to the x percent per annum rate of compound interest compounded half yearly, then what is the value (Approximate) of x ?

4.88 percent 

Rate 1 = 10%

Rate x% is compounded half yearly , 

So , Compound interest of 1 year = x + x + \(\frac{ x × x }{100}\)

= 2x + \(\frac{ x² }{100}\)

ATQ,

2x + \(\frac{ x² }{100}\) = 10

200x + x² = 1000

By solving ,

x = 4.88%