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:
Answer & explanation
Correct answer: option 3
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%