 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that, on what sum will compound interest for two years at 6% per annum be $74.15. The compound interest formula is amount A is equal to P into 1 plus R upon 100 raise to power n. Also, compound interest is equal to amount minus original principle. With this key idea, let us proceed with the solution. We need to find the sum of money on which the compound interest is $74.15 for two years at 6% per annum. So, let the sum of money be P. Let the amount after years be A. The rate of interest is equal to 6% per annum. Also, we are given the compound interest is equal to $74.15. The time n is equal to two years. Let the interest be equal to I. Compound interest is equal to amount minus principle. This implies I is equal to A minus P, which implies A is equal to I plus P. Now, as amount A is equal to P into 1 plus R upon 100 raise to power n, therefore, I plus P is equal to P into 1 plus R upon 100 raise to power n, which implies I is equal to P into 1 plus R upon 100 raise to power n minus P. As compound interest is given as $74.15, so $74.15 is equal to P into 1 plus 6 upon 100 raise to power 2 minus P, which is equal to P into 1 plus 6 upon 100 raise to power 2 minus 1 by taking P common. That is equal to P into 106 upon 100 raise to power 2 minus 1, which is equal to P into 53 upon 50 raise to power 2 minus 1, which can be written as P into 2809 upon 2500 minus 1, where 2809 is the square of 53 and 2500 is the square of 50. Taking the LCM, this is equal to P into 2809 minus 2500 upon 2500 equal to P into 309 upon 2500. This implies P is equal to 74.15 into 2500 upon 309, which implies P is equal to 185,375 upon 309. That is P is equal to 599.91, which is equal to 600 approximately. Hence, the sum of money is equal to $600, which is our answer. This completes our session. Hope you enjoyed the session.