 Hello and welcome to the session. In this session, we are going to discuss the following question and the question says that, find the compound interest on $300 for two years at 2.5% per annum interest being payable half yearly. Now, 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, P is equal to time. Amount is equal to principal plus interest. Compound interest is equal to amount minus original principal. With this key idea, let us proceed with the solution. Now, according to the question, we need to find the compound interest on $300 for two years at 2.5% per annum interest payable half yearly. Let the principal be equal to P which is equal to $300. Rate of interest is equal to 2.5% per annum which is equal to half of 2.5% per half year which is equal to 1.4% per half year. The time T is equal to which is equal to 2 into 2 which is 4.5 years. So, we will find the interest for four periods where the principal for each period will be equal to amount of the previous period. Now, the principal for the first period is equal to $300. As we know, simple interest is equal to P into R into T upon 100. Therefore, here the interest for the first period is equal to 300 into 5 by 4 into 1 by 100 which is equal to 15 by 4 dollars that is equal to 3.75 dollars. So, the amount for the first period is equal to $300 plus $3.75 that is equal to $303.75. Now, the principal for the second period is equal to the amount for the first period which is equal to $303.75. So, here the interest for the second period is equal to $303.75 into 5 by 4 into 1 by 100 dollars which is equal to $1518.75 upon $400. That is equal to $3.79. So, the amount for the second period is equal to $303.75 plus $3.79 which is equal to $307.54. So, again the principal for the third period will be equal to the amount for second period that is equal to $307.54. This implies the interest for the third period is equal to $307.54 into 5 by 4 into 1 by 100 dollars which is equal to $1537.7 upon $400. That is $3.84. So, amount for the third period is equal to $307.54 plus $3.84 which is equal to $311.38. Therefore, the principal for the fourth period is equal to $311.38. So, the interest for the fourth period is equal to $311.38 into 5 by 4 into 1 by 100 dollars which is equal to $1556.9 upon $400. That is equal to $3.89. So, the amount for the fourth period is equal to $311.38 plus $3.89 which is equal to $315.27. So, the amount after two years is $315.27 and the original principal is equal to $300. So, compound interest is equal to the amount minus the original principal which is equal to $315.27 minus $300. That is equal to $15.27. Hence, the compound interest after two years is equal to $15.27 which is our answer. This completes our session. Hope you enjoyed this session.