The Mathematics of Money

104 Chapter 3 Compound Interest

Assuming that this all works out all right with your calculator, you are likely to find that

entering everything at once is easier. The danger is the potential for a keystroke error when

entering such a lengthy expression. It is especially easy to misplace or forget the parenthe-

ses, a seemingly minor error with disastrous results. You may want to try working through

a few problems with each approach to see which you like best. Remember too that when-

ever you get an answer, you should ask yourself whether the numbers you end up with are

reasonable. A quick reality check will often, though not always, catch mistakes.

Let’s work through one more example. You may want to try evaluating the value both

ways to see which you like best. Of course, make sure that you choose an approach that

will give the correct answer with whatever model of calculator you are using.

Example 3.2.3 Find the future value of $85.75 at 8.37% compounded monthly for

15 years,

Since there are 12 months in the year:

i
0.0837___ 12 and n
(15)(12)
180

Plugging this into the compound interest formula we get:

FV 
 PV(1  i)n

FV
$85.75  1  0.0837___ 12 

180

We can evaluate this on the calculator as:

Operation Result

.0837/12


+1


^180


*85.75

0.006975

1.006975

3.494330151

299.64

Or:

Operation Result

85.75*(1.0837/12)^180= 299.64

Either way, the future value comes out to be $299.64.

Just as we saw in Section 3.1, we can use the formula to find the present value needed to

grow at compound interest to a desired future value.

Example 3.2.4 How much do I need to deposit today into a CD paying 6.06%

compounded monthly in order to have $10,000 in the account in 3 years?

Since interest compounds monthly, i 
 0.0606/12 and n 
 3(12) 
 36

FV 
 PV(1  i)n

$10,000
PV  1  0.0606___ 12 

36

$10,000
PV(1.19882570)

As in the past, we divide both sides through to get the PV. Also as in the past, using calculator

memory may make things easier.

PV 
 $8,341.50

So I need to deposit $8,341.50.

Comparing Compounding Frequencies

From everything we’ve seen so far, it seems reasonable to expect that the more often

interest compounds, the larger the total. This is in fact correct. The following example will

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