Intermediate Macroeconomics

Term paper - Part 3

3. Mortgage Rates

In Part 2 of this term paper you looked at the relationship between the median price of new homes and median household income. Hopefully you saw that over some periods home prices rose faster than income (the index was rising), slower than income (the index was falling), and that the current price/income ratio is the highest since at least 1967. The increase in income explains much but not all of the increase in prices over time.

Income represents only part of the affordability equation. The mortgage interest rate also plays a significant role. In fact you will find that when we account for the mortgage interest rate we might reach very different conclusions about the trend in home affordability.

Mortgage interest rates are reported by Freddie Mac ( In this part of the paper you will do something very similar to Part 2 -- calculate an index. This time you will calculate the annual mortgage plus interest payment as a percentage of median annual household income, i.e., what percentage of your gross income goes toward paying off the mortgage. So Part 3 includes a new graph and some observations about the graph and how they contrast with your observations in Part 2. While the data (mortgage interest rates) this time should be easier to find, the calculation of an index is more complicated.

Mortgage rates are generally quoted as a percentage plus "points". Points are the percent of the total loan amount that you must pay when you get the loan. For example, paying 2 points on a $100,000 loan means you must pay $2,000 (2 percent of $100,000) when you close the loan. You can get a slightly lower interest rate by paying more points. Generally it is recommended that you go for lower points rather than a lower interest rate. For example, if interest rates fall and you refinance your loan, your benefit is reduced if you "bought down" your original loan interest rate by paying higher points. Also, if you sell your house after owning it for only 5 or 10 years, you lose the remaining benefit of the lower interest rate that you paid for up front.

The monthly payment on a home covers repaying the original loan amount plus interest. We will ignore the additional payment required to cover home owners insurance and property taxes. We are implicitly assuming that insurance and taxes remain a fixed percentage of income and that only the mortgage payment (loan plus interest) varies as a percentage of income. The formula for the monthly mortgage payment is:

x = P • (1 + Z/100) •  (          - i / 1200        
1 - (1 + i/1200)360
  + i / 1200 )

x = monthly mortgage plus interest payment, dollars
P = the principal borrowed, dollars (e.g., the median price of new houses, 2001 = $175,200)
Z = "points" paid on a new home loan, percent (e.g., 2001 = 0.9)
i = 30-year conventional mortgage interest rate, percent (e.g., 2001 = 6.97)

Normally you would find the points paid included in a calculated "effective" interest rate. What we do here is add the points to the price of the home, P • (1 + Z/100), and take out a "no cash down" loan.

Note that the mortgage interest rate, i, is divided by 1200. What you are doing is first dividing the interest rate in percent by 100 to convert it to a fraction. Then you are dividing by 12 to convert it from an annual rate to a monthly rate. The interest rate in the denominator is raised to the power of 360. This simply corresponds to 30 years times twelve months, or 360 payments to be made.

For 2001 the calculation looks like:

x = 175200 • 1.009 •  (             6.97/1200          
1 - (1 + 6.97/1200)360
  + 6.97/1200 )

x = 176777 •   (      - 0.005808    
1 - (1.005808)360
  + 0.005808 )

x = 176777 •   (   - 0.005808 
1 - 8.0442
  + 0.005808 )

x = 176777 •   (  0.000824508 + 0.005808 )

x = $1,172.54

The above calculation was done in an Excel spreadsheet. You can check your calculations using one of many mortgage calculators available on the web. Google "mortgage calculator" for a list of sites.

Caution! When calculating the your payment/income index you must multiply the monthly mortgage payment by 12 before dividing by the median annual household income.

Affordability Index = monthly payment x 12 / median annual income

Note that I call it an "affordability index" rather than "mortgage payment/income index". This makes the text a little easier to read but it still distinguishes itself from the home price/income index from part 2.

So, part 3 just has three paragraphs and one graph:

3. New Home Affordability Index

Opening paragraph describing what this section is about.
Paragraph explaining how the U.S. new home affordability index is calculated and what it means (i.e., a high or increasing index value means homes are more or less affordable?)
Paragraph describing the time trend in the U.S. new home affordability index
Graph of time trend in the U.S. new home affordability index

What happened to the cross-section table? Since mortgage interest rates do not differ significantly across the country calculation an affordability index for cities would not reveal anything different from Part 2. Changes in mortgage interest rates may reveal much about changes in prices over time but don't explain differences across cities.