Math for Grownups (8 page)

After all, information—and organization—is power.

Because Crystal’s life is so organized and her clients are local, leasing is probably a good option for her. How much is she saving each month over the monthly cost of buying the car outright?

Let’s say Crystal is able to finance the car over 5 years at 4% interest. Using the monthly payment formula reveals that her monthly payment would be $651.02.

That’s more than twice her monthly payment on the lease!

$651.02
-
$311.04
=
$339.98

But remember that by leasing, Crystal will never own the car outright, and she’ll always have a car payment.

Then there’s the mileage restriction. If, in any year, Crystal goes over her allotted miles—which may be as few as 12,000 miles—she will have to pay up to 25¢ per mile. Thus if she drives the car 16,000 miles, she’ll owe as much as $1,000—or more than 2 months’ worth of lease payments.

The bottom line? Crystal will be responsible for the car during its most expensive years.

Deciding whether to buy or lease a car can seem overwhelming. And one of the reasons for this is that the math is complex. Finding the monthly payment on a loan or a lease requires the organizational skills of Martha Stewart! So if you’re more like Jack Black, here’s some help. Remember, multistep problems can be easier to solve if you ask a few simple questions.

1. What do you have?
List the information that you know. That includes any formulas you may need to use and the numbers that may be plugged into those formulas.

2. What do you want?
Write down the goal of the problem—finding the monthly payment or finding how much you can afford.

3. What can you do to make things easier?
No, the answer isn’t “get someone else to do it”! Here are some simple ideas: Draw a picture, make a chart, act out the problem, look for a pattern, list rules (like PEMDAS). And don’t forget to toss out any information that you don’t need. You won’t necessarily use every single number that you have.

4. Does the solution make sense?

When you find the solution, be sure to check it out. In other words, know what makes a reasonable answer.

Let’s say you’re trying to find the monthly payment on a $12,900 car loan. If you come up with $14,358.98, you’ve probably made a mistake somewhere along the line. Unless you’ve got the worst car loan in history, you’re not going to pay more than the car is worth each month. Likewise, if you find that your monthly payment is only $76.34, you may want to take another look at your calculations. It would be nice to have such a low monthly payment, but that’s not likely, given the price you are paying for the car.

On the Market: Buying a House by the Numbers

It’s the American dream. Perhaps you’re in the market for a house in the ’burbs with a picket fence and a big front porch. Or maybe you’re a city mouse, looking for shelter among row houses or modern condos. Heck, you could even be considering roughing it off the grid in a modest cabin in the woods.

Unless you’re renting a studio apartment in the Big Apple or are content living in your parents’ basement, buying a home is probably on your list of things to do as a grownup. But stepping into the real estate market can feel like jumping out of a perfectly good airplane. It’s downright scary.

That’s because most folks don’t have hundreds of thousands of dollars lying around. And that means one simple thing: When you buy a house, you agree to make a monthly mortgage payment.

Houses have big price tags. And mortgages are long-term commitments. But a few figures can give you the confidence to pull that parachute cord at just the right moment—and land safely on your feet.

You can’t get something for nothing, right? At least that’s what your mama always told you. And that’s why she wouldn’t approve of a zero-down mortgage.

Unless you’re a veteran with a Veterans Administration loan, you should expect to make a down payment on your house. And not just to please good old mom. The fact is, she has good reason to be suspicious of zero-down mortgages. When you skip the down payment, you’re borrowing a larger chunk of cash, which means a bigger monthly bill from your lender. But even worse is not having any equity in your home when you move in. If the real estate market goes south, you could find yourself “upside-down” on your mortgage—that is, owing more than the property is worth. In other words, if you had to sell your house, you wouldn’t get enough to pay back your lender. And that’s a scary situation.

Lenders really like down payments, too. Down payments say, “These buyers are trustworthy. They know how to save money. They’re serious about buying a house.”

But down payments are not just great for wooing the perfect lender. They also lower your monthly payment—which in turn lowers the amount of money that you’ll pay in interest on the loan
and
the total amount you’ll be shelling out over the life of the loan.

In short, making a $40,000 down payment up front can save you big bucks over 30 years.

Are you convinced yet?

There’s another reason to make a large down payment: private mortgage insurance, or PMI. Remember, your down payment says, “You can trust me.” A big down payment means the lender can
really
trust you. If you don’t have at least 20% to put down, your lender will require that you pay a little extra each month for insurance on your loan. This protects the lender in case you don’t make your house payments.

Just like a down payment on a car, the down payment on a house is a percent of the total price of the house. And just as in the purchase of a car, the amount you have for your down payment is one of the things that will affect how much house you can afford.

An example will probably help.

It’s been 10 years since you graduated. You have a great job and your college loans are all paid off. It’s time to take the next step: buying a house. You’ve been saving your bonuses for 7 years, and your latest bank statement shows a balance of $16,790. But by a stroke of good luck, that’s not all you have.

Nobody thought that ugly painting from your Aunt Martha was worth a thing, but you had a hunch. So when the popular television program,
Your Trash, My Treasure
came to town, you and a fraternity brother hauled it down to be appraised. Turns out you’ve got a good eye, because the darned thing is valued at about $40,000. Within a week, you sold it to a collector for $35,770.

With your savings, you have $52,560—that’s $16,790 plus $35,770. Looks like a great down payment on a house.

But how much house can you afford? Clearly, you’re no dummy, so you’re shooting for a 20% down payment.

20% of what is $52,560?

In
Chapter 2
, we talked about how to answer this question. If you’ve already read that chapter, you may remember that there are two ways to approach this problem: You can create and solve an algebraic equation, or you can remember a simple division problem.

If you don’t remember the shortcut, never fear. The algebra in this problem is very simple. All you need to do is remember some key terms.
Of
means multiplication;
what
is the variable (the answer you’re looking for); and
is
means “equals.” Translating and putting it all together, you get this equation:

0.20
x
= $52,560

To find
x
, you need to isolate it. That means you need to undo the multiplication. And to undo the multiplication, you need to do the inverse operation. Remember what
inverse
means? It means the opposite of something. Because the opposite of multiplication is division, that’s what you need to do. Simply divide each side of the equation by 0.20.

x
= $262,800

With a $52,560 down payment, then, you can afford to purchase a $262,800 house.

Now do you remember the shortcut? Just divide the down payment by the percent. (Hey! That’s what you did to solve the equation!)

You can use also the shortcut to figure out what you could afford if you only paid 10% down.

$52,560 / 0.10
=
$525,600

So, if you put 10% down, you can afford almost twice as much house, or a home worth $525,600. But be careful! There’s a heck of a lot more that goes into the mortgage. If you borrow more money, your monthly payment will be much higher.

In real estate,
equity
isn’t the union for professional stage actors. Nope, finding the equity you have in your home boils down to solving a simple subtraction problem:

Equity
=
the market value of the property
-
the outstanding mortgage balance

Unlike a car or a couch or anything else you might buy, real estate often appreciates in value. That’s why real estate is considered an investment—you may well earn money when you buy and later sell a house.

Down payments affect your equity. When you can make a large down payment, you reduce the amount of money you owe on the property. That means you have more equity from the very beginning.

Quite literally, make a $20,000 down payment on a house, you will have $20,000 in equity before you even move in!

That is a huge deal, especially if the real estate market goes south. If you need to sell your house quickly, but values have gone down, it helps to have some equity. At the very least, you may be able to break even—a much better deal than taking a loss. Having equity also enables you to take out a second mortgage, if you need to remodel or update your house. And if you wish to refinance your mortgage at a lower rate a few years down the road, having extra equity will help make that possible.

Before you even start shopping for a house, you’d better have a budget in mind; otherwise, you might find yourself looking around in a neighborhood that’s too rich for your bank account. Luckily, one little multiplication rule will help you estimate how much house you can afford.

It turns out that you should shoot for no more than five times your annual gross salary. If you gross $65,700 a year, for instance, your top limit should be 5 • $65,700, or $328,500. (And if your spouse or partner is also contributing to the family budget, you can add his or her salary, as well.)

Another important thing to consider is the current economy. In a poor economy, you should probably budget a smaller amount, just in case you get caught with a lower-paying job or, worse, with no job at all. And regardless of the economy, you should always consider how much debt you have. Not much? You may be able to handle a larger mortgage. A lot of debt? Do yourself a big favor and aim lower.

Gleaming hardwood floors, an attached garage, and a spectacular master suite may be the main attractions, but if you want to live in it, you have to be able to afford it. Forget the bells and whistles; you need a house with a monthly payment you can live with.

Naima has had enough of her neighbors’ loud music, loud parties, and loud arguments. It’s time for her to move out of the apartment complex she’s lived in since she left home after high school. She is more than ready for the peace and quiet of a single-family home and a little distance from her neighbors.

But can she afford to buy? Her monthly rent is $950, and with her recent promotion at work, she can add an additional $300 to that payment each month. Naima needs a monthly mortgage payment of no more than $1,250.

She has $17,450 in the bank for a down payment, and she’s prequalified for a loan: a 30-year mortgage with 4.25% fixed-rate interest. It was important for her to get prequalified for her mortgage, because the interest rate and the term (time period) of the loan play a part in how much she can afford. With a higher interest rate or a shorter time period, she could afford less. That’s because these factors increase the monthly mortgage payments.

Knowing that she can afford a monthly mortgage payment of $1,250, how much house can she buy without exceeding her monthly budget?

Naima can use one of hundreds of online mortgage calculators to figure this out. But she’s old school, and so she turns to the loan formula: