 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that calculate the compound interest on $4000 in one and a half years at 10% per annum compounded half yearly. Before we start the solution, let us review some formulas. Compound interest is equal to amount minus principal and amount is equal to p into 1 plus r by 2 upon 100 raised to part 2n compounded half yearly. 1 year is equal to 2 half years. Therefore r% per annum means r by 2% half yearly. N years means 2n half years. With this key idea, let us proceed with the solution. According to the question, we need to calculate the compound interest on $4000 in one and a half years at 10% per annum compounded half yearly. So here principal p is equal to $4000. The rate of interest r is equal to 10% per annum. r by 2 is equal to 10 by 2 which is equal to 5% half yearly. And time n is equal to 1 and a half years which is equal to 3 by 2 years. 2 into 3 by 2 is equal to 3 half years. As we know amount is equal to p into 1 plus r by 2 upon 100 raised to part 2n compounded half yearly. So here amount a is equal to 4000 into 1 plus 5 upon 100 raised to part 3. So this is equal to 4000 into 1 plus 1 by 20 raised to power 3. That is equal to 4000 into 20 plus 1 upon 20 raised to power 3 which is equal to 4000 into 21 upon 20 raised to power 3. This can be written as 4000 into 21 upon 20 into 21 upon 20 into 21 upon 20. So on cancelling all the zeros 2 times 2 is equal to 4. So this is equal to 21 into 21 into 21 upon 2 which is equal to 9261 upon 2. Which is equal to 4630.50 dollars. So amount a is equal to 4630.50 dollars. Now compounding trust is equal to amount minus principal. Therefore this is equal to 4630.50 minus 4000 dollars which is equal to 630.50 dollars. Hence compounding trust after 3 and a half years is equal to 630.50 dollars which is our answer. This completes our session. Hope you enjoyed this session.