 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that John has a recurring deposit account in the bank and deposits $140 per month for 4 years. If he gets $8092 on maturity, find the rate of interest given by the bank. The formula for simple interest is equal to P into R into T upon 100 where P is equal to the principal, R is equal to the rate of interest, T is equal to time. With this key idea let us proceed with the solution. Let P be equal to the installment or the money deposited per month which is equal to $140. Let N be equal to the number of months for which the amount is deposited that is equal to 4 into 12 which is equal to 48 months. Let rate of interest be equal to R% per annum. So the rate of interest will be equal to R by 12% per month. This John deposits $140 per month therefore he deposits $140 in the first month for 48 months. So the principal for first month is equal to 140 into 48. Again he deposits $140 in the second month for 47 months. So the principal for the second month is equal to 140 into 47. Moving on in this way he deposits $140 in the last month for one month. So the principal for the last month is equal to 140 into 1. So the equivalent principal for one month is equal to 140 into 48 plus 140 into 47 plus so on plus 140 into 1. This is equal to 140 into 48 plus 47 plus so on plus 1 which is equal to 140 into 48 into 48 plus 1 upon 2. As we know that 1 plus 2 plus 3 plus so on till N is equal to N into N plus 1 by 2. Now using the simple interest formula that is equal to P into R into T upon 100 simple interest is equal to 140 into 48 into 48 plus 1 by 2 into R upon 12 into 1 upon 100. This is equal to 140 into 48 into 49 into R upon 2 into 12 into 100. This is equal to 14 into 49 R upon 5 which is equal to 686 R by 5. The total deposit during 48 months is equal to 140 into 48 which is equal to $6,720. So the amount on maturity will be equal to $6,720 plus $686 R by 5. As we can see from the question the amount that John gets on maturity is $8092 so $8092 is equal to $6,720 plus $686 R by 5. This implies $686 R by 5 is equal to $8,092 minus $6,720. This implies $686 R by 5 is equal to $1,372 that is R is equal to $1,372 into 5 upon $686. As $686 into 2 is $1,375 so R is equal to 2 into 5 which is equal to 10% per annum. Hence rate of interest R is equal to 10% per annum which is our answer. This completes our session. Hope you enjoyed the session.