 Hello and welcome to the session. Let us discuss the following question. It says a man borrows rupees 36,410 from a finance company and has to repay it in three equal annual installments. Find the amount of each installment if the rate of interest is 10% per annum compounded annually. So let's now move on to the solution. We are given that the principal is rupees 36,410 and the rate of interest is 10% per annum and let each installment be equal to rupees x. Now let p1, p2 and p3 be the principal for the amount to be paid second and third year respectively. Therefore p1 is equal to rupees divided by 1 plus 10 upon 100 to the power 1. This is because amount A is equal to principal into 1 plus r upon 100 to the power n where A is the amount, p is the principal, r is the rate of interest and n is the number of years. So this implies p is equal to A divided by 1 plus r upon 100 to the power n. You must write this formula. P1 is equal to x divided by 1 plus 10 upon 100 to the power because p1 is the principal for the amount of rupees x to be paid at the end of the first year. So p1 is equal to rupees x divided by 1 plus 1 by 10 to the power 1 which is again equal to rupees x divided by taking LCM it would become 11 upon 10 to the power 1 or this is equal to rupees 10 by 11 into x. Similarly p2 will be equal to rupees 10 by 11 square into x and p3 will be equal to rupees 10 by 11 to the power 3 into x. Now p1 plus p2 plus p3 is equal to the principal. Now p1 is 10 upon 11 x, p2 is 10 upon 11 square into x, p3 is 10 upon 11 cube into x and p is 36410. Now take it 10 upon 11 x common we have 1 plus 10 upon 11 into 1 and here we have 10 upon 11 square into 1 and this is equal to 36410. Now again this implies 10 upon 11 into x into 1 plus 10 upon 11 plus square of 10 is 100 and square of 11 is 121 and this is equal to 36410. Now again this implies 10 upon 11 x into now taking LCM LCM would be 121 so we have 121 and in the numerator we have 121 plus 10 into 11 plus 100 is equal to 36410 becomes 11 x into 121 plus 110 plus 100 upon 121 and this is equal to 36410. Now again 10 upon 11 x into adding all these we have 331 upon 121 is equal to 36410 so this implies x is equal to 36410 into 121 into 11 upon 10 into 331 now 0 gets cancelled with 0 dividing 3641 by 331 gives us 11 so this implies x is equal to 11 into 121 into 11 so this implies x is equal to 121 into 121 11 into 11 is 121 so this implies x is equal to 14641 hence each installment is equal to rupees 14641 so this completes the question and the session. Bye for now take care have a good day.