time period receipts payments 0 $100,000 $2,000 1 0 $56,462 2 0 $56,461
(Using this method, loan origination fees, such as the cost of an appraisal and a credit report, can be treated exactly like discount points. In contrast, the APR ignores these fees as long as they are "customary." So two lenders who charge different fees can quote identical APR's.)
Next, however, suppose that we shorten the time horizon so that we pay back the loan after one year. We make a payment of $108,500 at that time, and the total discounted value of payments is $2,000 + $98636 = $100,636. At the shorter time horizon, the 8.5 percent loan with two points up front is more expensive than the 10 percent loan with no points.
Be careful interpreting this example, because the magnitudes are distorted by the simplicity of the two-year mortgage term. However, the basic lesson is that the time horizon affects the relative cost of mortgages when the discount rate is applied. The example correctly illustrates that a low-rate, high-point mortgage can be better at a longer time horizon but worse at a shorter time horizon.
The time horizon is the length of time that you expect to retain the mortgage. Choosing a ten-year time horizon does not mean that you will rule out a 30-year fixed rate mortgage, but it keeps you from over-estimating the advantage of the old stand-by.
The possiblity that you might move within ten years is not the only reason for choosing a shorter time horizon. You may expect your financial situation to change dramatically within ten years. If your income rises substantially, you may be able to pay off a mortgage sooner than 30 years; if you face college tuition expenses in five years, you may need to refinance. These are considerations that would lead to choosing a time horizon of 10 years or less.
It is important to remember that the interest rate on your ARM may rise by a different amount than the general interest rate increase in the scenario. Many ARMs start with low "teaser" rates, so that even in the scenario where market interest rates do not change your rate is likely to go up. Conversely, in the scenario where rates rise by 3 percent, your ARM will not necessarily go up by 3 percentage points when it first adjusts. Many ARMs have adjustment caps of 2 percent, so that your rate will adjust upward in stages under the high-rate scenario.
In our example, suppose that we have an ARM that is linked to the one-year rate. The hypothetical current value of the one-year rate is 7.8 percent, with a margin of 2.5 percent. That means that the rate on the ARM would be calculated as 10.3 percent if it were fully adjusted today. However, the ARM has an initial teaser rate of 9.5 percent, with no points. Moreover, it has a cap that says that the rate cannot go up by more than 2 percentage points.
Here is what the rate will be on our ARM next year under three scenarios:
scenario index margin cap rate constant rates 7.8 2.5 11.5 10.3 rates up 1 percent 8.8 2.5 11.5 11.3 rates up 3 percent 10.8 2.5 11.5 11.5* *the rate would be 13.3, but it is limited by the cap
Payments under the three scenarios would be time period rates constant rates up 1 rates up 3 1 $57,231 $57,231 $57,231 2 $57,653 $58,175 $58,280
If you've gotten this far, then you probably will enjoy working with The Intelligent Mortgage Agent.
Win $1000 off the cost of your move! Enter when you use The Moving Calculator (TM).