The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

must be expressed in months, and so we must multiply it by 12 (since there are 12 months

per year.) So

i 
 _____0.06 12 
 0.005

and

n 
 7(12) 
 84

Substituting these into the formula we get:

FV 
 PV(1  i)n

FV 
 ($2,500)(1  0.005)^84

FV 
 $3,800.92

Let’s work through a second example to get comfortable with how this works.

Example 3.2.2 Find the future value of $3,250 at 4.75% simple interest

compounded daily for 4 years.

Since there are 365 days in a year, we must divide the annual rate by 365 to get a daily rate,

and multiply the term in years by 365 to get the term in days.

i 
 0.0475_______ 365 
 0.000130137

and

n 
 4(365) 
 1,460

Substituting these values into the formula we get:

FV 
 PV(1  i)n

FV 
 $3,250(1.000130137)^1460

FV 
 $3,930.01

In Example 3.2.2 the value of i unfortunately did not come out to a nice neat value the way

it did in Example 3.2.1. This will often happen, especially with daily compounding, since

few numbers divide by 365 evenly. It is important to be careful with rounding in these

cases. Since i is so small, it must be carried out to many decimal places to avoid significant

rounding errors. (For example, if we had rounded to four decimal places and used i 


0.0001, our answer would have come out to be $3,760.86, which is pretty far off the mark.)

The value of i should always be taken out to the full number of decimal places given by

your calculator. (The number of decimal places on your calculator may be more or fewer

than those shown in this text, but as long as you take the value to your calculator’s full

precision there will be no problems.)

Tediousness (and potential for errors due to typos) can be avoided by finding the

value of n first. Then, when we find i, we can just leave that number stored in the

calculator, add 1, raise the result to the n power, and multiply by the PV. If your

calculator does not have order of operations built-in, the keystrokes (after finding n)

would then be:

Operation Result

.0475/365


+1


^1460


*3250

0.000130137

1.000130137

1.20923465

3930.01

If your calculator recognizes order of operations, the entire formula can be entered all at

once.

Operation Result

3250*(1.0475/365)^1460= 3930.01

3.2 Compounding Frequencies 103