Simple interest on a sum of money, at 5% per annum for 2 years, is Rs.50. The compound interest on the same sum for the same period at the same interest rate is:

Correct option is B

Given:

Interest =₹50

Rate of interest = 5%

Time =2 years

Formula Used:

​$$SI = \frac{P\times R\times T}{100}$$​​

Compounded Amount = $$Principle \times \left(1+ \frac{r}{100}\right)^{t}$$​​

Compound Interest = Amount - Principle

Solution:

Let the Principle be P, then SI:

​$$50 = \frac{P\times 5\times 2}{100}$$​​

P =₹500

Compounded amount =$$500 \times \left(1+ \frac{5}{100}\right)^{2}$$​ 

=$$500 \times \left( \frac{21}{20}\right)^{2}$$​​

​$$= 500 \times \left( \frac{441}{400}\right)$$​​

= ₹551.25

Interest = 551.25 -500 = ₹51.25