Alondra is offered two loans for $5000 to buy her first car. She can borrow from the First Math Bank at a rate of only 7% for a five-year loan, or she can
borrow from Bank of the Proportions at a rate of 11% for a 3-year loan,
Part 1: How much would she pay in interest for each bank?
First Math Bank:
Bank of the Proportions:
Part 2: From which bank should Alondra borrow money if she wants to pay the
least amount of interest?
First Math Bank or Bank of the Proportions

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.