 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that, the compound interest on a certain sum for two years is 630 dollars and the simple interest for the same period is 600 dollars. Find the principal and rate of interest. We know that simple interest is equal to p into r into t upon 100 where p is equal to the principal r is equal to the rate of interest t is equal to time. With this key idea let us proceed with the solution. According to the question we need to find the principal and the rate of interest for which the compound interest on a certain sum of money for two years is 630 dollars and the simple interest for the same period is 600 dollars. The simple interest for two years is given to us as 600 dollars. So the simple interest for one year is equal to 300 dollars. As we know the compound interest and simple interest for the first year is equal therefore compound interest for first year will be equal to 300 dollars. As the total compound interest was 630 dollars this implies that compound interest for the second year will be equal to 330 dollars. So now the simple interest on 300 dollars for first year is equal to 330 minus 300 dollars which is equal to 30 dollars as simple interest is equal to p into r into t upon 100 therefore 30 will be equal to 300 into r into 1 upon 100 where r is equal to the rate of interest which we need to find. So r is equal to 30 into 100 upon 300 which is equal to 10. So r is equal to 10 percent per annum. Now we have time is equal to 1 year rate is equal to 10 percent per annum. Simple interest is equal to 300 dollars. So this implies that 300 is equal to p into 10 into 1 upon 100 where p is equal to the principle which we need to find. So p is equal to 300 into 100 upon 10 which is equal to 3000 dollars. Hence the rate of interest r is equal to 10 percent per annum and the principle p is equal to 3000 dollars. This is our answer. This completes our session. Hope you enjoyed this session.