 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that Mrs Smith deposited $350 per month in a bank for one year and three months under the recurring deposit scheme. If the maturity value of her deposit is $5,565, find the rate of interest per annum. 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. According to the question we need to find the rate of interest per annum if Mrs Smith deposited $350 per month in a bank for one year and three months and the maturity value of her deposit is $5,565. Let the sum deposited per month P is equal to $350, the number of months N is equal to one year, three months which is equal to 15 months. Let the rate of interest be equal to R% per annum that is equal to R by 12% per month. Now she deposits $350 in the first month for 15 months so the principal for the first month is equal to 350 into 15. Again she deposits $350 in the second month for 14 months so the principal for second month is equal to 350 into 14. Moving on in this way she deposits $350 in the last month for one month so the principal for the last month is equal to 350 into 1. Therefore the equivalent principal for one month is equal to 350 into 15 plus 350 into 14 and so on plus 350 into 1. So this is equal to 350 into 15 plus 14 plus so on plus 1 that is equal to 350 into 15 into 15 plus 1 upon 2. As we know 1 plus 2 plus so on plus N is equal to N into N plus 1 by 2. So now using the simple interest formula simple interest is equal to P into R into T upon 100. So we have simple interest is equal to 350 into 15 into 15 plus 1 upon 2 into R by 12 into 1 upon 100. So this is equal to 350 into 15 into 16 into R upon 2 into 12 into 100. This will be equal to 5 7's are 35, 5 2's are 10, 2 8's are 16, 2 4's are 8, 3 4's are 12 and 3 5's are 15. So this is equal to 7 into 5 R which is equal to 35 R. Now the total deposit during 15 months is equal to 350 into 15 which is equal to 5,250 dollars. As in the question the maturity value of a deposit is 5,565 dollars. So amount on maturity is equal to 5,565 dollars which is equal to 5,250 plus 35 R dollars. This implies 35 R is equal to 5,565 minus 5,250 which implies 35 R is equal to 315. This implies R is equal to 315 upon 35. So here 5 times 7 is 35, 5 times 63 is 315 and this is equal to 9. Hence the rate of interest R is equal to 9 percent per annum which is R answer. This completes our session. Hope you enjoyed the session.