You know that in one year you are going to buy a house. The annual interest rate for fixed-rate 30-year mortgages is currently 6.00%, and the price of the type of house you are considering is $120,000. However, things may change. Using your knowledge of the economy (and a crystal ball), you estimate that the interest rate might increase or decrease by as much as one percentage point. Also, the price of the house might increase by as much as $10,000—it certainly won’t decrease. You assess the probability distribution of the interest rate change as shown in the file S04_39.xlsx. The probability distribution of the increase in the price of the house is also shown in this file. Finally, you assume that the two random events are probabilistically independent. This means that the probability of any joint event, such as an interest increase of 0.50% and a price increase of $5000, is the product of the individual probabilities.
a. Using Excel’s PMT function, find the expected monthly house payment (using a 30-year fixed-rate mortgage) if there is no down payment. Find the variance and standard deviation of this monthly payment.
b. Repeat part a, but assume that the down payment is 10% of the price of the house (so that you finance only 90%).
c. Is the independence assumption realistic?