 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says A man deposited rupees 10,000 in a bank at a rate of 5% simple interest annually Find the amount in 15th year since it deposited the amount and also calculate the total amount after 20 years Let's now begin with the solution and money deposited let us denote it by P principle that is rupees 10,000 Rate of interest let us denote it by R as 5% per annum and let us denote the time period of 1 year by T So the simple interest on rupees 10,000 at the rate of 5% for 1 year will be given by P into R into T upon 100 That is 10,000 into 5 into 1 upon 100 which is equal to rupees 500 Therefore amount after 1 year will be equal to the principle plus the interest which is equal to rupees 10,500 Similarly amount is equal to rupees amount after first year interest for 1 year on rupees 10,000 which is rupees 500 So this is equal to rupees 11,000 Amount after third year is equal to rupees amount after 2 years that is 11,000 plus again 500 which is the interest on rupees 10,000 for 1 year So this is equal to rupees 11,500 Therefore amount in this account in the first, second, third, fourth and so on years in the first year the amount is 10,000 After 1 year the amount becomes 10,500 Then 11,000 after second year or in the third year Then we have 11,500 which is after third year and so on Now as we can see this is an AP series whose first term that is denoted by small a is 10,000 And the common difference small d is equal to 500 And we have to find the amount in 15 year that is we have to find the 15th term of this AP series And it's formula is a plus 15 minus 1 into d and a is 10,000 plus 14 into 500 Which is equal to 10,000 plus 7,000 which is equal to 17,000 And therefore amount in 15th year is equal to rupees 17,000 Also we have to find the amount after 20 years So let us find the amount after 20 years That is we have to find the 21st term of the series and that will be a plus 21 minus 1 into d So that is 10,000 plus 20 into 500 Which is equal to 10,000 plus 10,000 or this is equal to 20,000 And therefore amount to 20 years is equal to rupees 20,000 And hence our answers are the amount after 15 years is 17,000 rupees And the amount after 20 years is 20,000 rupees So this completes the session take care and have a good day