 Hello and welcome to the session. In this session, we are going to discuss the following question and the question says that, Sam made an investment of $10,000 in his business. In the first year, he incurred a loss of 5%. However, during the second year, he earned a profit of 6% which in the third year rose to 10%. Calculate the net profit for the entire period. The compound interest formula is A is equal to P into 1 plus R upon 100 raise to power n. We know that value of yearly growth factor is 1 plus R upon 100 and value of yearly decay factor is 1 minus R upon 100. With this key idea, let us proceed with the solution. According to the question, Sam made an investment of $10,000 in his business. He had a loss of 5% in the first year. However, during the second year, he earned a profit of 6% which in the third year rose to 10%. We need to calculate the net profit for the entire period. Let the investment made by Sam be P which is equal to $10,000. Let R1 be the yearly loss which is equal to 5%. Let R2 be the yearly profit that is profit in the second year which is equal to 6% and R3 be the yearly profit that is profit in the third year which is equal to 10%. As Sam incurred a loss of 5% in the first year, so we shall use the yearly decay factor in the compound interest formula for the first year. As he had a profit of 6% in the second year and 10% in the third year, so we shall use the yearly growth factor for the second and third year in the compound interest formula. So amount after 3 years will be is equal to P into 1 minus R1 upon 100 into 1 plus R2 upon 100 into 1 plus R3 upon 100. So amount is equal to 10,000 into 1 minus 5 upon 100 into 1 plus 6 upon 100 into 1 plus 10 upon 100 dollars. Taking the LCM within the brackets, this is equal to 10,000 into 100 minus 5 upon 100 into 100 plus 6 upon 100 into 100 plus 10 upon 100 dollars which is equal to 10,000 into 95 upon 100 into 106 upon 100 into 110 upon 100. Now here first we cancel out all the zeros. Now 5 into 2 is equal to 10 and 5 into 19 is equal to 95 then 2 into 53 is 106. So this is equal to 19 into 53 into 11 dollars which is equal to 11,077 dollars. So the net profit will be 11,077 minus 10,000 dollars which is equal to 10,077 dollars. Hence the net profit is equal to 10,077 dollars which is our final answer. This completes our session. Hope you enjoyed this session.