 Hello and welcome to the session. In this session, we are going to discuss the following question. The question says that calculate the compound interest due in two-and-a-half years on $6,000 at 10% compound interest. Let us see some of the formulas that we are going to use for this question. Simple interest is equal to P into R into T upon 100 where P is equal to the principle R is equal to the rate of interest and T is equal to the time in years. Amount is equal to principle plus interest and compound interest is equal to the amount minus the original principle. With this key idea, we shall proceed with the solution. Now, according to the question, we shall calculate the compound interest due in two-and-a-half years on $6,000 at 10% compound interest. So, to calculate the compound interest for two-and-a-half years, we shall first find the simple interest for first year, second year and at last for the last half year where each time the principle will be the amount at the end of the previous year. For the first year, principle P is equal to $6,000, rate of interest R is equal to 10% and the time T is equal to one year. Now, as we know, simple interest is equal to P into R into T upon 100. Therefore, interest for first year is equal to $6,000 into 10 into 1 upon $100, which is equal to T into $10, that is $600. Now, as amount is equal to principle plus interest, therefore amount at the end of first year is equal to $6,000 plus $600, which is equal to $6,600. Now, we shall find the interest for the second year. The principle P for the second year is equal to $6,600, which is the amount at the end of previous year. The rate of interest is equal to 10% and the time T is equal to one year. As interest is equal to P into R into T upon 100, therefore interest for the second year is equal to $6,600 into 10 into 1 upon $100, which is equal to $66 into $10, that is $60. Now, the amount at the end of second year is equal to principle plus interest, that is equal to $6,600 plus $660, that is equal to $7,260. Now, we have found the interest for the first year and for the second year, so we shall find the interest for the last half year. Here, the principle P is equal to $7,260, which is the amount at the end of previous year. The rate of interest R is equal to 10% and time T is equal to half year. So, interest for the last half year is equal to $7,260 into 10 into 1 upon $100 into $2, which is equal to $726 upon $2. That is equal to $363, so the amount at the end of the last half year is equal to principle plus interest, that is equal to $7,260 plus $363. This is equal to $7,623. So now, amount in two and a half years is equal to $7,623 and the original principle is equal to $6,000. Therefore, compound interest for two and a half years is equal to amount in two and a half years minus the original principle, that is equal to $7,623 minus $6,000 which is equal to $1,623. So finally, we have compound interest for two and a half years is equal to $1,623 which is our answer. This completes our session. Hope you enjoyed the session.