Understanding the Mathematics of Personal Finance

A FEW LAST WORDS

When interest rates go down, it’s time to investigate opportunities for refinancing your home. This means that you look for a new mortgage loan that will replace your old mortgage loan at a lower interest rate. In many cases, the up-front costs of the new loan are very low (sometimes even 0). As always, folding the up-front costs into the new loan gives you an effective interest rate and a resulting monthly payment number.

There are some “gotchas” in refinancing a home that you have to keep in mind. Let’s say that you are 15 years into a 30-year mortgage and the opportunity comes along to refinance at a lower rate. If the new loan is a 15-year loan, then you’ll see that your monthly payments drop and that your home is paid off 15 years after financing, which is when the original (30-year) mortgage would have been paid off. If you take a new 20- or 30- year mortgage loan, your payments will drop even further, but you might be signing a contract that requires you to make payments well into your intended retirement. Work through the numbers and make sure you want to do this; don’t be seduced by the lower monthly payments.

Using the same scenario as above, after 15 years of payments, you’ve built some equity[21] in your home, and in good economic times, home values usually increase over time, further building equity in your home. This gives you the opportunity to refinance for more money than you owe on your first mortgage and therefore to “walk away” with some money.

Whether or not doing this is a good idea depends on just how you use the money. My point here is that you should always work through the numbers and really under­stand all sides of what you’re doing when you make major financial decisions.

A few paragraphs ago I slipped something by that is true but can be looked at in a number of ways depending on your perspective. Consider a fixed rate, 30-year mortgage loan taken for $350,000 at 8% interest. The monthly payment is $2,568.18. At the end of 15 years, the outstanding balance is $267,959. Let’s say you refinance and take a new 15-year loan for $300,000, giving yourself almost $32,000 in cash to use as you wish. This doesn’t mean that your monthly payments will now be higher than they used to be. If you can get the new loan for 6.23%, your new payments are (to within about a dollar) the same as the old payments. If you can get the new loan for less than 6.23%, then your payments are lower than they used to be.

You might think of this $32,000 as “free money” because you continue making the same monthly payments that you’ve always made, with the loan being fully paid off at the same time as originally planned. However, when you refinanced, the equity in your home dropped by the $32,000 that you took away as cash. This $32,000 drop will diminish gradually for the next 15 years, reaching 0 at the last payment of the loan. However, if you sell your house sometime during this second 15-year period, you will walk away with less money than if you had never taken the $32,000.

In the next chapter (Chapter 9), I will discuss about the effects of taxation and inflation on savings and long-term loans such as mortgages. Very briefly here, the principal effect of taxation on a mortgage loan for your home is that, at least today and with some qualifying details, the interest is deductible from your federal (IRS) taxes. If you can estimate your taxable income, you can estimate a lower effective interest rate for your home mortgage.

Inflation, on the other hand, raises the prices of things that you need to or want to buy, thereby making your dollar less valuable. This is bad news for how much your savings will be able to buy in the future. If you’re lucky enough to have a job or a business that allows your income to climb along with inflation, you are paying off your home mortgage with cheaper dollars (i. e., a smaller percentage of your salary) every year.

PROBLEMS

1. Consider a fixed rate, fixed payment 15-year mortgage loan for $350,000. I’ll consider the present value of the loan when I take the loan to be my actual cost of the loan. If I want

to keep this present value constant at about $400,000, how much can I borrow based upon the APR of the loan? Assume the savings interest rate is one-half of the loan APR.

2. Find the monthly payments for the above situation, using APRs of 0%, 2%, 4%, 6%, 8%, and 10%. Then divide each monthly principal by its accompanying payment, giving you the ratio of principal : payment.

3. In this chapter, I argued that the best choice for a loan is the loan with the lowest present value, subject to the constraint that you have to be able to afford the payments. We could consider a figure of merit (FM) for a loan as the product of the present value and the monthly payment—when both of these factors are low, the FM will be low; when both are high, the FM will be high; and intermediate cases will fall somewhere in between. Using the data in Table 8.2, calculate the FM for each loan and discuss whether or not this FM definition is good.

In the table, I got the FMs by multiplying the PV by the Monthly Payment and then dividing by 10,000,000. These divisions don’t change the relative values of the FMs, but they do make it a lot easier to read the significant figures of the numbers without getting distracted by all of the digits. [22] [23]