Mortgage myths

Mortgage myths

Following a good discussion on the topic of mortgage, I would like to share a few myths:

The first year the payment is almost all interest. Your friends and your brokers keep telling you that the first year you will be paying a high portion of interest on your loan. What does that mean? Actually nothing! Many people interpret this in the wrong way. They don’t want to refinance again because the payments for the first few years contain higher percentage of interests. Once you passed the first few years, your payment include more principle and less interests. If you refinanced again, your payment will contain higher portion of interests again, thus disadvantage.  Their reason is that they are paying a lot of interest payments, so it seems a waste to refinance again because they think all the interest payments they made did not count anything.

Well let me explain to you, there is no disadvantage for the first year. Why? The US government regulates the mortgage industry with clear disclosure, they can not cheat on you. If your APR is stated as 5%, then it is 5%. As long as you borrowed x amount money from your lender, you pay 5% on the x amount interests. You don’t pay more, you don’t pay less either, it is very fair. If you think you are paying a higher percent than this 5% for the first year, then you are wrong. It is against the law to charge more. So don’t explain to people that the first few years’ payments contain high interests, it does not help anyone, instead explain to people this: when you have x amount of borrowed money in your procession for one day, you need to pay interests on the x amount for that day based on APR, no more and no less.

Mortgage interest is tax deductible thus there is a higher equivalent return. The question asked is this: if you have x amount of money, would you pay down the mortgage with y percent interest or would you invest in a mutual fund with z percent gain? A lot of people would answer the question saying that mortgage interest is tax deductible, making complicated mathematical formulas. It is true that because the mortgage tax is deductible, even you pay y percent interests to mortgage company, you would will get some money back from IRS at the tax time. Thus people believe that if they invest their money instead, they should target a tax equivalent gain much higher than the mortgage interests rate so that it is fair comparison. Below we will demonstrate the tax equivalent gain theory is wrong in this situation. If we ignore the situation that the capital gain may put you to a higher tax bracket, then we should only compare whether y is greater or smaller than z without considering the tax factor.  That is: if z is greater than y, then you should invest in the mutual fund even if you have to pay the capital gains  tax on it.

Here is the math.

option 1: pay down x amount to your mortgage. The result is zero: result=0.

option 2: not pay down x amount at interest rate of y, invest the x amount to yield z percent.


we explain each term below:

-x*y  =this is the interests you pay. It is negative because it is going out of your pocket

+x*y*T1=this is at the end of the year, you are getting the money from IRS. “T1” is ordinary income tax rate.

+x*z=this is the investment yield

-x*z*T2=this is the capital gain you have to pay IRS. T2 is either interests income or capital gain income tax rate.

Thus if y=z, and if T1=T2, then the result =0. If T1>T2, then result > 0.  This means when the y=z, it is always better to invest your money.

In summary:

1. if you mortgage rate is y, don’t think about tax equivalent issue when you are making your decision.

2. instead, simply compare the mortgage rate y with the investment gain z directly, if z is equal or greater than y, then don’t pay down your mortgage, invest the money to something else for z percent.