The compound interest and the amount obtained, on a certain sum of money are Rs.820 and Rs.8200 respectively after 2 years. If the rate of interest compounded yearly, then the rate of interest is:

5%

Formula used-

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

Here, Amount = Rs 8820, Rate = R%, t = 2 years  and compound interest = Rs. 820

Compound interest = Amount - Principal

Principal = 8820 - 820 = 8000

8820 =  8000$(1 \;+\; \frac{R}{100})^2$

⇒ \(\frac{8820}{8000}\) = $(1 \;+\; \frac{R}{100})^2$

⇒ \(\frac{441}{400}\) = $(1 \;+\; \frac{R}{100})^2$

⇒ ( \(\frac{21}{20}\) )² = (  1 + \(\frac{R}{100}\) )²

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

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

⇒ Rate = 5%