Math for Grownups (23 page)

Glenda has decided to get tough on herself. She really needs to pay off her credit card in 3 years, and she has $17,000 to go. What monthly payment should she make?

She may drive a BTV, but Glenda doesn’t have bubbles on the brain. She uses the monthly payment formula (from
Chapter 2
) to find her answer.

(Did you notice that the formula is slightly different here than in
Chapter 2
? That’s because of the way the variables are defined. Keep reading, and you’ll see that
r
is the
monthly
interest rate in this version of the formula.)

First, she needs to understand the variables. Glenda has used this formula before—to find the monthly payments on that brand new BMW that she thought was a good idea a few years ago. (Dumb thing didn’t go very fast!) Anyway, she knows that

M
is the monthly payment

P
is the amount owed on the loan

r
is the monthly interest rate

n
is the number of months in the period of the loan

With her favorite pink, feathered pen, she gets to work, defining her variables:

Now she can use the formula.

Glenda has a good handle on her order of operations, thanks to Please Excuse My Dear Aunt Sally. And she remembers that
So even without a scientific calculator—it didn’t come in purple—she can find the solution.

First, she deals with that negative exponent.

Now Glenda finds 1.015
³⁶
.

Next, she starts handling the parentheses, beginning with the one in the denominator of the fraction.

She finishes off the calculations in the denominator:

And divides.

M
= 17,000 • 0.036

Finally, she can multiply to find her monthly payment.

M
= $612

“Well!” Glenda breathily exclaims. “That seems manageable!” She makes plans to skip her weekly tea with the mayor of Munchkinland and reduce her hoopskirt budget by half.

“That should do it!” she twinkles. And hops in her BTV to share the good news with the Wizard.

If interest were not compounded, these formulas would be a heck of a lot simpler. When you compound interest, you earn interest on the interest.

Compound interest is great for savings accounts, but not so wonderful for credit card balances. When interest is compounded on debt, you are
paying
interest on the interest. But when the interest on your savings is compounded, you
earn
interest on the interest.

Simple interest is the opposite: not so great for savings, but terrific for credit card balances. You
earn
less on a savings account earning simple interest than on an account earning compound interest. But you
pay
less on a debt that is earning simple interest than on one earning compound interest.

To find the amount due on a loan that earns compound interest, you need to know a few things: the amount of the loan, the interest rate, and the number of compounding periods. Then you can use this handy-dandy amount-due formula:

A
=
P
(1 +
r
)
n

A
is the total amount due

P
is the principal

r
is the interest rate per compounding period

n
is the number of compounding periods

That’s a lot to think about, but if you break things down, it’s not so bad.

You borrowed $3,500 at 6% interest compounded monthly. If you paid off the loan in 1 year, how much did you pay in all?

The principal is $3,500—that’s easy enough. But finding the rest of the variables requires a little more work. Because you paid off the loan in a year and the interest is compounded monthly, the number of compounding periods is 12. That means the interest rate per compounding period is 6% / 12, or 0.5%.

A
= 3,500(1 + 0.005)
¹²

A
= 3,500(1.005)
¹²

A
= 3,500•1.06

A
= $3,710

What if you had a simple-interest loan? You’d use this formula instead:

I
=
Prt

I
is the total amount of interest

P
is the principal

r
is the interest rate

t
is the length of the loan in years

Substituting, you would find

I
= 3,500 • 0.06 • 1

I
= $210

So you would owe $210 in interest, bringing your total payment to $3,500 + $210, or $3,710.

But about the only place you can get a simple-interest loan is from Mom and Dad.