**Finance Excel***

Consider the following situation: each individual borrower has a probability every month of missing a payment on a mortgage. Say the probability of missing a payment is 1%, and the probability making up a past-due payment is 0.1%. If the borrower misses 3 months of payments, we'll say the borrower "defaults" and never makes a payment again.

(a) Write out the transition matrix between Current, Delinquent-1, Delinquent-2, Delinquent-3, and Default. The key feature of this matrix is that most of the transition probabilities are 0, because the borrower can only transition between "adjacent" states. In other words, the probability of jumping from Delinquent-1 to Delinquent-3 is 0, etc.

(b) Without doing it, how would you use the techniques we have discussed to simulate the following question? "Plot the fraction of a pool of 1,000 borrowers who have defaulted over time?" (Answer is a 3-5 sentence paragraph.)

(c) What if I told you that borrowers with FICO score over 700 are much less likely to miss a payment than borrowers with FICO score < 700. If you knew the FICO score of every borrower, how would your answer to (b) change?

Please show the formulas from excel and you will get a thumbs up. Much gratitude.