Math for Grownups (10 page)

With a 15-year mortgage, he would have made 180 monthly payments (15 • 12), so the total payment would have been

$920.73 • 180

$165,731.40

How much would Drew have saved if he’d gone with a 15-year mortgage? All he needs to do to find out is subtract the total paid for the 15-year mortgage from the total paid for the 30-year mortgage.

$211,680
-
$165,731.40

$45,948.60

By spreading out his mortgage payments over 30 years, instead of 15 years, Drew ended up paying almost $50,000 more. That’s more than most people earn in a year!

(How about if we don’t tell Drew. In this case, ignorance is bliss.)

When you shop for a mortgage—or any kind of loan, for that matter—you should listen for three little magic letters: APR, which stands for annual percentage rate. That’s the number most often associated with mortgages and other loans.

When a newspaper article touts mortgage rates at 4.5%, that’s the APR. And when you see a commercial that advertises a car dealer’s 6% financing, that’s the APR.

The A for “annual” is the star here. Any third grader can tell you that
annual
means something that happens once a year. But mortgages and other loans are usually compounded monthly. That means the interest is calculated each month and added to the balance of the loan. (You’re paying interest on the interest.)

And this means you need to be careful with your formulas. The
r
in a formula may stand for the APR, or it may represent the interest rate per month.

This all comes down to
reasonable answers
. Everybody makes mistakes. Everybody misunderstands things from time to time. When you put everything into a formula and come up with an answer that doesn’t make sense, go back.

Unless you’ve got the world’s worst mortgage, you shouldn’t be paying $123,450 a month on a $100,000 house.

It’s terrific if you can get a fixed interest rate. That means your interest rate won’t go up—or down—for the life of the loan. But with some mortgages, the interest rate won’t stay put. These are called adjustable-rate mortgages, or ARMs.

With an ARM, the initial interest rate stays the same for a specified period of time. Then it will periodically go up or down.

• 1-1 ARM: fixed rate for 1 year, adjusts every year after that

• 3-1 ARM: fixed rate for 3 years, adjusts every year after that

• 5-1 ARM: fixed rate for 5 years, adjusts every year after that

But where do these adjustments come from? Can the mortgage lender simply jack up the rate from 6% to 20%? No way.

Changes in interest rates are dictated by something called an economic index. There are dozens of economic indices (the plural of
index
) so it’s a good idea to consider which one the lender is using when you’re shopping for an ARM. Fluctuations in rates are affected by a variety of forces, including the health of the economy, as well as supply and demand. For example, when the number of houses on the market is up and the economy is down, rates are typically lower.

Every ARM will have an interest cap, or a limit on how high the interest can get. This may be a periodic cap (a limit on the amount the interest rate can increase from period to period) or an overall cap (a limit on the amount the rate can increase over the life of the mortgage). If you had an ARM with a periodic interest rate cap of 2%, your interest could not go up more than 2% each adjustment period. So, if your interest rate were 8%, the highest it could get in the next adjustment period would be 10%. And in this example, if you had an ARM with an overall cap of 5%, your interest rate would
never
go over 13% (or 8% + 5%).

The interest rate of an ARM also includes something called the
margin
. This is an extra charge that the lender adds on to the rate to cover its costs and profits. Good news! Unlike interest rates, on an adjustable-rate mortgage, margins usually stay the same over the life of the loan.

Here’s the bottom line: When you have an ARM, your monthly payments can change. This should make perfect sense. If interest is part of your monthly payment, changes in the interest rate will make the payment go up or down.

Why would anyone want a mortgage with monthly payments that might fluctuate from year to year?

A lot of times, the initial rate for an ARM is less than what you can get for a fixed-rate mortgage. If you don’t expect to own the house for very long, you can save big bucks with an ARM. And lower interest rates mean lower monthly payments. So you could afford pricier digs with an ARM.

Finally, any increases in your income can cover higher monthly payments. So if you’re expecting a big pay raise or a higher-paying job, an ARM might be a good option.

You don’t have to spring for a short-term mortgage to reduce the total you pay for your house. And guess what? The total-payment formula shows you how.

T
=
Mn

Remember that equations are like teeter-totters—the equals sign means the sides must be balanced. So if you want
T
to be smaller,
Mn
must be smaller too, right?

In any loan, there are three variables that affect how much your monthly payments are (and also how much your total payment is). We talked about this in
Chapter 2
, but to review, here they are:

P
is the principal, or the amount borrowed

r
is the monthly interest rate

n
is the number of months in the loan

If you can reduce any of these, you will reduce the total loan payment.

To reduce the principal, you can buy a different house, negotiate a lower price, or increase the size of your down payment. We’ll leave that up to you (and your real estate agent). But you can also reduce the monthly interest rate and the number of months in the loan in other ways.

First, let’s look at the interest rate. Just like looking for the best deal on a car or a flat-screen TV, you want to shop around. The lower the interest rate, the less you’ll pay on the loan altogether.

Prove it, you say? Here’s an example. Let’s say you’re borrowing $325,000 to buy a house. You have the choice of two 30-year mortgages—one has a 6.25% interest rate and one that has a 6.75% rate. To find out how much you would pay for either loan, you can use a formula, or you can turn to an online mortgage calculator. Let’s make things easy this time with an online mortgage calculator.

You’ll pay $2,001.08 each month for the first mortgage (the one with a 6.25% interest rate). That’s a total of $720,388.80 over the life of the mortgage. And you’ll pay $2,107.94 each month for the second mortgage (the one with a 6.75% interest rate)—a whopping $758,858.40 over the life of the mortgage.

That tiny difference in the interest rate adds up to a huge difference in the end.

But there’s another way to limit the amount you’ll pay in interest. When you buy a home, you’ll probably have the option of buying points (sometimes called discount points), which is essentially a way to prepay the interest rate. You pay for points when you sign the final mortgage contracts. Why would you do that, you ask?

When you buy discount points, you lower the interest rate on your mortgage. How nifty is that?

Each discount point costs 1% of the mortgage amount and lowers the interest rate on a 30-year fixed rate mortgage by about 0.125% (or 1/8 of 1%), although this can vary.

Buying a point (or two points or ten points) is even more valuable than it sounds.

Let’s look at an example with nice, round numbers.

To buy the house you’ve got your eye on, you’ll have to take out a mortgage loan for $100,000. Because a discount point equals 1% of the loan amount, each point costs $1,000. If you have a 30-year fixed-rate mortgage with 7.5% interest, purchasing one point will lower your rate to 7.375%. (That’s because 7.5% - 0.125% = 7.375%.)

Using a mortgage calculator, you can find that buying a point reduces your monthly mortgage payment from $699.21 to $690.68, leaving you with an extra $8.53 in your pocket every month.

That doesn’t seem like a lot of money, but over the life of the mortgage, it can add up! Even in the first year, you would save $8.53 • 12, or $102.36.

And over the life of the mortgage, you would save $8.53 • 360, or $3,070.80. (Remember, there are 360 months in 30 years.)

In short, when you reduce
r
, you can lower your total payment.

What else can you change? That’s right—
n.

You can do this a couple different ways, but they all boil down to one thing—paying off your mortgage early. It turns out that there’s a really crafty way to do this. See if you can figure this out by answering some very simple questions.

1. How many months are there in a year?

2. How many weeks are there in a year?

Most mortgages are paid monthly. Because there are 12 months in the year, you make 12 payments a year. However, if you made your mortgage payment every 4 weeks instead of every month, you’d make 13 payments a year (52 weeks / 4 = 13). What many people do is split their monthly payment in half and pay that half-payment every 2 weeks. (This works especially well for people who get paid every 2 weeks instead of on fixed days of the month). Thus, if your mortgage payment were $1,000 per month, and you paid $500 every 2 weeks, you’d make 26 half-payments in the year, or 13 full payments.

That’s an extra mortgage payment each and every year.

Here’s the math:

Hannah has a monthly mortgage payment of $1,300. That means she pays $15,600 each year for her mortgage.

If she decides to make biweekly payments instead, she’ll send in $650 every other week. That translates to 26 payments of $650 each year, for a total of $16,900.

That’s $1,300 more a year than Hannah is paying with monthly payments, which means she’ll pay off her mortgage faster.

It’s not like you’re tricking the bank with these payments. You’re actually tricking yourself, by spreading out an extra monthly payment over the entire year. For most folks, that’s a heck of a lot easier than writing an extra check at the end of the year.
Note:
Some loans don’t allow prepayment (which is what this essentially is) or impose penalties for prepayment, so make sure your mortgage terms allow you to do this.

Just because you can buy points, should you? Well, of course not.

First, you need to know whether the savings will be more than the cost. If you buy a point for $1,000 and save $2,948.40, you’ll end up pocketing $1,948.40. (Which could very well be worth it.)

Another thing to consider is the break-even place. That’s the number of months you must keep the loan to break even on paying points. This calculation is pretty simple: Just divide the amount charged for discount points by the monthly savings.

For example, if you paid $1,000 for a point to save $8.19 per month, your break-even place would be

$1,000 / 8.19

122.1

This means that your points purchase will “pay off” if you keep the loan for
more than
122 months (or 10 years 2 months).

And if the time to your break-even place is longer than the life of the loan? That’s a pretty obvious indication that spending so much on points is just not worth it.

When you buy discount points, you pay for them in one lump sum, at the closing. So why not put that money toward the down payment instead?

You may want to think about that—and here are some questions that can help:

1.
How long will you be in the house?
 If you’re planning to sell your house before you break even, adding to your down payment makes more sense. However, if you’re planning to keep the mortgage for a long time, buying points may be the better option.

2.
Do you need a tax deduction?
Uncle Sam offers an incentive for buying points: As of this writing, you can deduct the entire cost of discount points from your taxes in the year that you buy your house. Otherwise, that deduction is spread out over the time that you have the mortgage. So, if you need a tax deduction right away, buy the points.

3.
Do you have enough money for the down payment?
Some lenders require a 20% down payment, so you may not have a choice at all.

4.
Will a larger down payment affect the type of loan you can get?
If you want a 30-year fixed-rate loan, you’ll probably need to make a large down payment.

5.
Which will lower your monthly payments more: increasing your down payment or buying points?
A little bit of math can help you keep some cash in the bank (or under your mattress).

When you close on the purchase of a house, bring your checkbook. Unless you’ve negotiated something different with the seller, you’ll have to lay down some cash before the deal is done.

Here are some of the costs you might be expected to cover at closing:

•
Processing fees
cover the administrative costs of processing your loan. These include expenses incurred in checking your credit report, the lender’s attorney’s fees, document preparation costs, and so on.

• You already know what
points
are: a one-time charge that you may pay in order to lower your interest rate over the life of the mortgage.