 Hello and welcome to the session. In this session, we are going to discuss the following question and the question says that Mr. William needs $8000 after four years. What least amount of money per month must be put in a recurring deposit account in order to get the required money at the required time? The rate of interest being 11.5% per annum. The formula for simple interest is P into R into T upon 100. With this key idea, let us proceed with the solution. According to the question, we are given the maturity value that is $8000 after four years. And we need to find the principal per month to get the required money at the required time for which the rate of interest is 11.5% per annum. So here the period of deposit that is n is equal to four years which is equal to 48 months. The rate of interest R is equal to 11.5% per annum which is equal to 11.5 upon 12% per month. The amount of maturity is equal to $8000. Suppose the money deposited by Mr. William per month is equal to P dollars. That means he deposits P dollars in the first month for 48 months. So the principal for first month is equal to P into 48 which is equal to 48 B dollars. He again deposits P dollars in the second month for 47 months. So the principal for the second month is equal to P into 47 which is equal to 47 B dollars. And so on he deposits P dollars in the last month for one month. So the principal for the last month is equal to P dollars into one which is equal to P dollars. So now the equivalent principal for 48 months is equal to 48 P plus 47 P plus so on P dollars. This is equal to P into 48 plus 47 plus so on plus 1 which is equal to P into 48 into 48 plus 1 upon 2. As we know 1 plus 2 plus so on till n is equal to n into n plus 1 by 2. So now we have the principal for 48 months and the rate of interest per month is 11.5 upon 12%. Using the formula simple interest is equal to P into R into T upon 100. We have simple interest is equal to P into 48 into 48 plus 1 upon 2 into 11.5 upon 12 upon 100. As the time is one month. So this is equal to P into 48 into 49 upon 2 into 12 into 11.5 upon 100. So this is equal to P into 2 into 49 into 11.5 upon 100 which is equal to 1127 P upon 100. So simple interest is equal to 11.27 P dollars. Now the total money deposited by Mr. William is equal to P into 48 which is equal to 48 P dollars. Therefore amount on maturity is equal to 48 P plus 11.27 P dollars which is equal to 59.27 P dollars. As we are given the amount of maturity is 8000 dollars. Therefore 8000 dollars is equal to 59.27 P dollars which implies P is equal to 8000 upon 59.27. That is equal to 134.97 dollars which is equal to 135 dollars approximately. Hence Mr. William deposited 135 dollars per month which is our answer. This completes our session. Hope you enjoyed the session.