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# Pay the Points?

Typically, American mortgage lenders will offer potential borrowers a menu of loans, each of which bears an interest rate and an extra amount of "interest" that the borrower must pay at the inception of the loan. This extra prepaid interest is generally referred to as "points" and is computed as a stated fraction of the initial loan balance. The menu generally permits the borrower to "buy down" the interest rate by paying points. If the borrower thinks he or she will hold the underlying real estate for a long period, it is often a good idea to pay points. On the other hand, if the borrower thinks he or she is likely to sell the underlying real estate in the near future, points are often not a good idea.
This Demonstration permits you to compare two loans with different interest rates and points and to determine the conditions under which one is superior to the other. You can select the amortization period of the loan, "q" (the fraction of time into the loan when the underlying asset is sold and the loan is thus accelerated), and the rate of interest you can earn on money you invest. The Demonstration responds with a contour plot that shows the discounted value of the cash flow that results from each of the proposed mortgages. In general, locations in the lower left of the contour plot are better for the borrower than locations in the upper right. By moving the locator objects in the contour plot, you can control the interest rates and points of the two loans under comparison. The locator object colored green is better for the borrower than the one colored red. The Demonstration also produces a grid summarizing the situation.

### DETAILS

The two bottom-left 2D sliders in the Demonstration permit you to zoom in on areas of interest. The first one lets you set the lowest interest rates and points to be examined. The second one lets you set the range of interest rates and points to be examined. These controls should be used with some care since you can become confused by zooming into areas in which no loans are available.
This Demonstration assumes that interest rates are fixed for the lifetime of the loan. Adjustable rate mortgages create additional complexities not addressed in this Demonstration.
This Demonstration ignores the tax consequences of both mortgage interest payments and investment income. It is intended to illustrate concepts involved in mortgage lending. Persons actually intending to borrow money to purchase real estate should consult financial professionals to determine which sort of loan products are best for them in light of taxation and other issues.
If the borrower's discount rate is less than the interest rate on a mortgage, the borrower would likely do better to prepay the mortgage than invest the funds. The mortgage interest rates thus generally set a floor on the sensible discount rates to use.
Tooltips are used throughout this Demonstration to help explain various controls and outputs.
Snapshot 1: if the underlying asset is held for a short period of time, the no points loan proves better than the high points loan, even though the latter has a lower interest rate.
Snapshot 2: if the underlying asset is held for a long period of time, the no points loan proves inferior to the high points loan.
Snapshot 3: the code underlying this Demonstration can handle a wide range of scenarios.

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