Auppose that at the end of a month, a customer owes a bank K1500. In the middle of the month, the customer pays Kx to the bank where x<1000, and at the end of the month the bank adds interest at a rate of 4% of the remaining amount still owed. This process continues every month until the money owed is repaid in full. (i) Find the value of x for which the customer still owes 1500 at the start of every month
(ii) find the value of x for which for which the whole amount owed is paid off exactly after the second payment
(iii) show that value of x for which the whole amount owed is paid off exactly after the (n+1)th payment is given by
where r=1.04