 Hello and welcome to the session. Let's work out the following problem. It says a loan of rupees 4200 is to be returned into equal installments. If the rate of interest is 10% per annum compounded annually, calculate the amount of each installment. So let's now move on to the solution and let amount of each installment be equal to rupees X. Now we know that the amount is given by the formula P that is principle into 1 plus R upon 100 to the power N that is A is equal to P into 100 plus R upon 100 to the power N. So this implies P is equal to A into 100 upon 10 plus R to the power N where R is the rate of interest and is the number of years. You must remember this formula. Now we have assumed that amount of each installment as rupees X. So at the end of the first year present value that is principle P1 is equal to X that is amount into 100 upon 100 plus R R is 10% to the power 1 since N is the number of years. So here it is end of the first year This is the present value. So now we have X into 100 upon 110 that is X into 10 upon 11. Now similarly at the end of second year present value is or the principle is P2 is equal to amount of installment into 100 upon 110 to the power 2 that is X into 10 upon 11 to the power 2. Now according to question the loan is of rupees 40 to 100. So some of these two principles is rupees 42 P1 plus P2 is equal to 4200. So we have X into 10 upon 11 plus X into 10 upon 11 to the power 2 is equal to 4200. Now taking X into 10 upon 11 common we have 1 plus 10 upon 11 is equal to 4200. This implies X into 10 upon 11 into taking calcium we have 11 plus 10 upon 11 is equal to 4200. So this implies X into 10 upon 11 into 21 upon 11 is equal to 4200. So this implies X is equal to 4200 into 11 into 11 upon 10 into 21. Zero gets cancelled with zero and 21 into 20 is 4 20. So we have 20 into 11 into 11 which is equal to 4,000, 2,420. Therefore amount of each installment is equal to rupees 2,420. So this completes the question and the session. Why for now take care. Have a good day.