EXAMPLE 7 A 30-Year Mortgage on a Median-Priced Home

Suppose that you are a family with the U.S. median household income of about $53,000 and you want to buy a median-priced home for $205,000, with a 30-year fixed-rate, federally insured mortgage at 3.25% (the data are for the beginning of 2015). Recall that the median (discussed in Section 5.4, pages 196–200) means that half are below and half are above. Suppose that you can make a down payment of only $7000 (just above the minimum of 3.5% required), plus pay closing costs of about $4000. Can you afford such a home?

Mortgage lenders have “affordability” guidelines that suggest that a family cannot afford to spend more than 31% of its monthly income on housing. Thus, by these guidelines, you can afford per month.

What is the monthly payment on the loan? The principal is , the monthly interest rate is , and months. The amortization payment formula gives a monthly payment of

919

Well, that sounds good. Unfortunately, there is more to the mortgage than just the amount needed to amortize the loan. Your payment will also have to cover real estate taxes, mortgage insurance, and homeowner’s insurance on the property. On a $198,000 home, these may add $500 or more to the monthly payment, which will then total about $1362.

It’s really close! So, the median household may just barely be able to afford the median-priced home (depending on the area of the country), even while interest rates I remain at record lows.