Money and
Understanding 
Mortgages and Christmas Gifts (December 20, 2012) Summary: Making extra payments towards a longterm debt (such as a mortgage) can shorten the time it takes to pay off the entire debt, resulting in significant savings, even if the extra payments are small. The higher the interest rate, the more you end up saving. It's the beginning of December. A husband, a wife, and two children are about to spend a total of $600 on holiday gifts to give to one another. Then a friend gives them an idea: "You are about to buy gifts that have limited longterm value. Instead, why don't you lower your gift budget to $100, and use the extra $500 to pay down your mortgage?" So, my gentle reader, what do think? Is this good advice? The answer is yes. Whenever you make an extra payment towards a long term debt — even a relatively small payment once a year — the extra money can significantly shorten the time it takes to pay off the entire debt. This, in turn, will save you more that you might think. In fact, I think it's safe to say that when you see the actual numbers you will be astonished. Before we get to that, however, I need to spend a few minutes discussing mortgages and how they work. Understanding Your Mortgage The basic idea behind a mortgage — or any longterm borrowing — is that money is worth money. That is, if you are going to make use of someone's money for a long period of time, you are going to have to pay them a fee. The fee you pay is called "interest"; the money you owe is the "principal". When you sign a mortgage contract, you agree to make monthly payments for a certain amount of time, for example, 30 years, 20 years, or 15 years. Depending on they type mortgage you have, the interest rate will always be the same, or it may change from time to time depending on certain conditions. If the interest rate is always the same, you have a "fixedrate mortgage"; if it can change, you have a "variable rate mortgage". Let's take a look at how the system works for the most common mortgage: a 30year loan with a fixed rate of interest. With a 30year mortgage, you promise to make 360 monthly payments in a row (30 years x 12 months/year). The amount of the payment is the same every month, and is calculated mathematically so that, if you make all 360 payments, the last payment pays back the very last dollar that is owed. In other words, the very last payment reduces the principal to zero. As a general rule, you have the right to make an extra payment for as much as you want, whenever you want. The advantage of making an extra payment is that it reduces the principal which, ultimately, lowers your total cost. As you will see, this can save you a significant amount of money. Let's consider a specific example. You buy a house that costs $375,000. You make a 20% down payment of $75,000, which means you must borrow $300,000 ($375,000$75,000). To do so, you take out a 30year mortgage at an interest rate is 4% a year, which is 0.33% a month (4%/12). Your monthly payment is calculated mathematically to be $1,432. Every month, you must pay 0.33% of your outstanding balance in interest. This is money you never see again. Whatever is left over is used to reduce the principal. Month #1: The interest you pay is 0.33% of $300,000, which is $1,000. Your monthly payment is $1,432. If you subtract the interest from $1,432, you have $432 left over to reduce the principal. Thus, after you make the first payment, you owe $299,568 ($300,000$432). Month #2: The interest you pay is 0.33% of $299,568, which is $999. Your monthly payment is $1,432, which means that after paying the interest for the month, you have $434 left over to reduce the principal. Thus, after you make the second payment, you owe $299,134. You can see this pattern in Table 1, which shows you what happens as you make the first 12 payments: 
Table 1: Amortization Schedule Sample — First 12 Months (4%)

Look carefully at the table and you will notice something striking. At the beginning of a mortgage, most of your monthly payment is not used to reduce your principal. Instead, most of the payment is used to pay interest! Indeed, in the first year (the first 12 payments above), an average of 69.3% of everything you pay is interest. This is money you will never see again. Only 30.7% of the money you pay is actually used to reduce your principal. This is why it takes so long to pay off the entire mortgage. The table above illustrates what economists call "amortization": the idea that when a loan is paid back in installments, the principal (the amount owing) decreases every time a payment is made. A complete table, showing all the payments required to pay back a loan is called an "amortization schedule". I'm not going to show you the full amortization schedule for the 30year mortgage, as it would be 360 lines long (30 years x 12 months/year). However, in case you are wondering what the last year of the mortgage looks like, Table 2 shows the end of the amortization schedule, that is, the final 12 payments. 
Table 2: Amortization Schedule Sample  Final 12 Months (4%)

Notice that, during the last year of the mortgage, the principal is so low that that very little of the monthly payment is needed for interest. Specifically, in the last year, an average of only 2.1% is needed to pay interest. This means that 97.9% of the payments are used to lower the principal. Why Interest Rates Are So Important to You At this point, we are almost ready to answer the question I posed earlier: Would it be a good idea for a family with a mortgage to reduce the amount they spend on holiday gifts and use the savings to pay off part of their mortgage early? Before we answer the question, however, I want to take a moment to show you how important the interest rate is when you borrow money for a long time. In the example above, we assumed an interest rate of 4% per year. Historically, this is actually an extremely low rate. You can see this in Table 3, which shows the average interest rates in the United States, for each decade since the 1970s. These rates are for 30year fixedrate mortgages.
As you can see, the interest rates in the 2010s are very low. In fact, my research shows that interest rates in the 2010s are the lowest ever in the history of longterm, fixedrate mortgages. To show you how much of a difference this makes, let's consider an example where you borrow the same amount of money as above, but at 12.7%, the average interest rate for the 1980s. As is our previous example, you buy a house that costs $375,000, with a 20% down payment of $75,000. You then take out a 30year mortgage for $300,000 ($375,000$75,000). In this case, however, the interest rate is 12.7% a year or 1.06% a month (12.7%/12). In our previous example, at 4% interest, your monthly payment was $1,432. At 12.7% interest, your payment increases to $3,248. Thus, over the life of the mortgage (360 months), you are required pay $3,248 every month instead of $1,432, an increase of $1,816. A natural question to ask is — aside from a possible tax deduction — what do you get for the extra money? The answer is, you get nothing! Although you are required to pay $3,248 every month, you are still paying back the same amount of money ($300,000) over the same amount of time (30 years). To show you how much of a difference this makes, Table 4 shows you the first year of the amortization schedule for the same loan we discussed above, but with an interest rate of 12.7%: 
Table 4: Amortization Schedule Sample — First 12 Months (12.7%)

As we saw earlier, at 4% interest, your first payment was 69.8% interest and 30.2% principal. At 12.7% interest, your first payment would be 97.7% interest and only 2.3% principal! As you can see, the interest rate in effect at the time you borrow the money has an important effect on your mortgage. To quantify this, the table below shows how much more you would end up paying in interest over 30 years, when you compare 12.7% to 4%. Table 5: Comparison of Money Paid, 4% vs. 12.7%
Notice that in both cases, you borrow $300,000 and you pay back $300,000. However, with an interest rate of 12.7%, you end up paying an extra $653,815 ($1,169.424  $515,609) over the 30year time period. In fact, by the time you have made all 360 payments, you will have paid 3.9 times the amount you borrowed in the first place. This is because the mortgage will have cost you a total of $869,424 in interest. Putting Your Christmas Savings to Work We are now ready to answer the original question. Let's use the following example. A family has just bought a house for which they borrowed $300,000, using a 30year fixed rate mortgage with a 4% interest rate. It is December, and they must make their first payment. At the same time, the family is about to spend $600 on holiday gifts. Would it be a good idea to reduce this to $100, and put the extra $500 towards the mortgage? As you saw in our first example, the monthly mortgage payment is $1,432. When the family makes the first payment, $1,000 is interest, which means that $432 is available to go towards the actual loan. Thus, after the first payment, the amount they owe decreases from $300,000 to $299,568. (You can see all these numbers in Table 1 above.) It happens, however, that the family decides to cut down on their holiday spending to save $500, which they send in as a onetime extra payment. This reduces the amount they owe by $500, from $299,568 to $299,068. Thus, when it comes time to make the second payment, they owe less money than they would otherwise. This means that the interest is a bit lower, which means more money is available to go towards paying back the loan. This sounds good, but it gets even better. What if the family decides to reduce their holiday gift expenditures for more than one year and use all the extra money to pay down the mortgage? The more years they do this, the more they end up saving over the life of the mortgage. The results are shown Table 6. Table 6: Savings from extra payments, 4% interest
As you can see, if the family makes a single, onetime $500 payment at the very beginning of their mortgage, they will end up saving $1,650. If they pay an extra $500 for the first five years, they will save $7,579. If they do it for 10 years, they will save $13,689. This is looking better and better, but notice what happens when we push it as far as we can. Suppose that the family decides to make this a permanent habit. They agree that, from now on, they will spend only $100 on holiday gifts and that, every December, they will pay an extra $500 towards the principal on their mortgage. The savings on the mortgage are now significantly larger. In fact, the family will end up saving $28,046 (and it will cost them only $15,000). So far, all these numbers assume a 4% interest rate. However, what if we do the same analysis for an interest rate of 12.7%, such as was common in the 1980s. The results will surprise you. Table 7: Savings from extra payments, 12.7% interest
Isn't this astonishing? A family that, in the 1980s, bought a house with a $300,000, 30year fixedrate mortgage with an interest rate of 17.4% (the going rate at the time) could save $77,609 over the life of the mortgage simply by making one extra $500 payment at the very beginning of the mortgage. If the family made one extra $500 payment every year over 30 years, they would pay a total $15,000 extra, but end up saving $313,428, which is $13,428 more than they borrowed in the first place! Longterm Benefits vs. Shortterm Pleasures You might think that most people, most of the time, make reasonable decisions so as to get the most for their money. However, this is often not the case, particularly when it comes to weighing shortterm pleasures against long term benefits. Although spending a lot of money on the holidays is an American custom, let us be realistic: the pleasure it brings us is both limited and transitory. In fact, soon after the gifts are opened — no matter how expensive they might be — our level of happiness returns to what it was before the holidays. I imagine that, by now, you are convinced of the importance of getting as low a mortgage rate as possible, as well as the wisdom of making extra payments, even small ones, whenever you can. At the risk of being accused of being a Scrooge ("Bah humbug!"), I would like to make the following suggestion: This year, take the time to think carefully and consider the numbers. Talk to your family about creating a winter holiday based on gratitude, togetherness, and celebration. If you decide to do so, you will find that it will cost you a lot less than buying expensive gifts for everyone. You can then take the money you saved and use as an extra mortgage payment. I realize that the extra payment may not seem like much now. However, I promise you that, later in life, it will be a big deal and you will be glad you did it. And that, my gentle reader, is my holiday gift to you.
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