 Hello and welcome to the session. In this session, we are going to discuss the following question and the question says that, find the amount and interest of $30,000 in one and a half years at 10% per annum compounded half-yearly. The compound interest formula is amount A is equal to P into 1 plus R upon 100 raised to power N. If payable half-yearly, one year is equal to two half years, therefore R% per annum means R by 2% half-yearly. Also, N years means two N half years. Compound interest is equal to amount minus original principle. So, with this key idea, let us proceed with the solution. According to the question, we need to find the amount and the interest of $30,000 in one and a half years at 10% per annum compounded half-yearly. So, we are given the principle P equal to $30,000. The time T is equal to one and a half years which is equal to 3 by 2 years that will be equal to 2 into 3 by 2 that is 3 half years. So, we have N is equal to 3 half years. The rate of interest R is given as 10% per annum. This implies R by 2% is equal to 10 upon 2% that is equal to 5% half-yearly. As we know, amount A is equal to P into 1 plus R upon 100 raised to power N. So, here the amount is equal to 30,000 into 1 plus 5 upon 100 raised to power $3 which is equal to 30,000 into 1 plus 5 upon 100 raised to power $3. Which is equal to 30,000 into 100 plus 5 upon 100 raised to power $3. That is equal to 30,000 into 105 upon 100 raised to power $3 which is equal to 30,000 into 21 upon 20 raised to power $3. So, this can be written as 30,000 into 21 upon 20 into 21 upon 20 into 21 upon 20. Now, cancelling the zeros first 2 into 15 is 30. This will be equal to 15 into 21 into 21 into 21 upon $4 that is equal to 138,915 upon $4. Which is equal to 34,728.75 dollars as compound interest is equal to amount minus principal. So, here the interest will be equal to 34,728.75 minus 30,000 dollars which is equal to 4,728.75 dollars. Hence, the amount is equal to 34,728.75 dollars and the interest is equal to 4,728.75 dollars which is our answer. This completes our session. Hope you enjoyed the session.