The compound interest on ₹4,000 after 3 years is ₹630.50. Then the rate of interest compounded yearly is :

5%

The formula that we used here is :-

Compound interest = Amount - Principal

Compound interest = P$(1 \;+\; \frac{R}{100})^t$ - P

630.50 = 4000 [ ( 1 + \(\frac{R}{100}\) )³ - 1 ]

\(\frac{1261}{8000}\) =  [ ( 1 + \(\frac{R}{100}\) )³ - 1 ]

\(\frac{1261}{8000}\)  + 1 = ( 1 + \(\frac{R}{100}\) )³ 

\(\frac{9261}{8000}\)  = ( 1 + \(\frac{R}{100}\) )³ 

( \(\frac{21}{20}\) )³  = ( 1 + \(\frac{R}{100}\) )³ 

So, \(\frac{21}{20}\) =  1 + \(\frac{R}{100}\)

\(\frac{R}{100}\) = \(\frac{1}{20}\) 

R = 5%

So, rate is 5%.