# solution

Over the past 40 years, interest rates have varied widely. The rate for a 30-year mortgage reached a high of 14.75% in July 1984, and it reached 3.31%, in November, 2012. A significant impact of lower interest rates on society is that they enable more people to afford the purchase of a home. In this exercise, we consider the purchase of a home that sells for \$125,000. Assume that we can make a down payment of \$25,000, so we need to borrow \$100,000. We assume that our annual income is \$40,000 and that we have no other debt. We determine whether we can afford to buy the home at the high and low rates mentioned at the beginning of this paragraph. a. What is our monthly income? b. Lending agencies usually require that no more than 28% of the borrowerâ€™s monthly income be spent on housing. How much does that represent in our case? c. The amount we will spend on housing consists of our monthly mortgage payment plus property taxes and hazard insurance. Assume that property taxes plus insurance total \$250 per month, and subtract this from the answer to part b to determine what monthly payment we can afford. d. Use your answer to part c to determine how much we can borrow if the term is 30 years and the interest rate is at the historic high of 14.75%. Can we afford the home? e. Use your answer to part c to determine how much we can borrow if the term is 30 years and the interest rate is 3.31%. Can we afford the home now? f. What is the difference in the amount we can borrow between the rates used in parts d and e?

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