 Hi and welcome to the session. Let's work out the following question. The question says a loan of Rs 10,815 is to be returned in three equal half yearly installments. Calculate the amount of each installment if the rate of interest is 13-1 by 3% per annum compounded half yearly. Let us start with the solution to this question. Let amount of each installment be equal to P loan amount BS be equal to Rs 10,815 that is given to us in the question. Now rate of interest say small r is equal to half of 13-1 by 3% because it is given to us that it is compounded half yearly. This will be equal to 40 by 3 into 1 by 2 that is equal to 20 by 3%. Number of installments be equal to 3 and we denote it by small n. Therefore s will be equal to 100 into P divided by r multiplied by 1 minus 1 plus r upon 100 the whole raise to power minus n. This is equal to, this is same as 10815 is equal to 100 P divided by 20 by 3 into 1 minus 1 plus 20 divided by 3 into 100. The whole raise to power minus 3 or 10,815 is equal to 3 into 100 P divided by 20 multiplied by 1 minus 1 plus 1 upon 3 into 5 the whole raise to power minus 3. This is same as 10,815 is equal to 3 into 5 P because 100 divided by 20 is 5 multiplied by 1 minus 15 plus 1 divided by 15 and the whole raise to power minus 3. Or 10,815 is equal to 15 P multiplied by 1 minus 16 upon 15 the whole raise to power minus 3 or 10,815 is equal to 15 P into 1 minus. Now this is same as 15 by 16 the whole raise to power 3 or 10,815 is equal to 15 P into 1 minus. Now cube of 15 is 3 3 7 5 divided by cube of 16 that is 4096 or 10,815 is equal to 15 P multiplied by 791 divided by 4096 or P is equal to 10815 multiplied by 4096 divided by 10. Now here we see that we have 721 in the numerator so here we have 15 into 721 this is equal to 721 multiplied by 4096 divided by 721 because 10815 divided by 15 is 721. Now this gets cancelled with this and we have 4096 thus each value of installment is rupees 4096 so I hope that you understood the solution and enjoyed the session have a good day.