Currently, you owe the bank TL 9.800 for a car loan. The loan has an interest rate of 7,75% per year with monthly compounding. You were making payments of TL 310 for each ending month. Your bank has recently changed such that you can no longer afford to make these TL 310 payments. After talking withyour bank officer and explaining the situation, he has agreed to lower your monthly payments to TL225 while keeping the interest rate at 7,75 % per year with monthly compounding. Determine how much longer it will take you to repay this loan than you had originally planned with this new payment schedule.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.