The Mathematics of Money

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

account balance under compound interest is not only growing, but it is growing at an

accelerating rate!

Looking back to the problems from Chapters 1 and 2, it is worth noting that, with

few exceptions, the terms have generally been fairly short, with most under 1 year and

very few extending further than 2 or 3 years. The reason for this should now be apparent.

A lender would have to be quite foolish to pass up the opportunity to profit from the power

of compounding over the long term. Even on this 5-year example, the advantage (to the

lender) of compounding is obvious.

What about even longer terms? There is certainly every reason to expect that the gap

between simple and compound interest will continue to widen. What if, instead of 5 years,

we consider our $5,000 at 8% for 50 years? It is no trouble to see what the account would

grow to under simple interest:

I 
 PRT

I 
 ($5,000)(0.08)(50)

I 
 $20,000

and so the account would grow to a total of $25,000, which doesn’t sound too bad for a

$5,000 investment.

Yet we know that under compound interest you would fare even better. How much

better? Before we actually try to calculate the difference, it’s worth venturing a guess.

Could the difference be as much as double the balance, or $50,000? $100,000 would be

4 times as much, which would be a huge difference. But, in fact, these guesses are both far

too low, as can be seen from Table 3.1:

TABLE 3.1 Comparison of Simple and Compound Interest

Assumptions: $5,000 deposited at 8% interest; compound interest is compounded annually.

(Continued)

3.1 Compound Interest: The Basics 89

SIMPLE INTEREST COMPOUND INTEREST

Year Start Interest End Start Interest End

Difference in

End Balance

1 $5,000.00 $400.00 $5,400.00 $5,000.00 $400.00 $5,400.00 $0.00

2 $5,400.00 $400.00 $5,800.00 $5,400.00 $432.00 $5,832.00 $32.00

3 $5,800.00 $400.00 $6,200.00 $5,832.00 $466.56 $6,298.56 $98.56

4 $6,200.00 $400.00 $6,600.00 $6,298.56 $503.88 $6,802.44 $202.44

5 $6,600.00 $400.00 $7,000.00 $6,802.44 $544.20 $7,346.64 $346.64

6 $7,000.00 $400.00 $7,400.00 $7,346.64 $587.73 $7,934.37 $534.37

7 $7,400.00 $400.00 $7,800.00 $7,934.37 $634.75 $8,569.12 $769.12

8 $7,800.00 $400.00 $8,200.00 $8,569.12 $685.53 $9,254.65 $1,054.65

9 $8,200.00 $400.00 $8,600.00 $9,254.65 $740.37 $9,995.02 $1,395.02

10 $8,600.00 $400.00 $9,000.00 $9,995.02 $799.60 $10,794.62 $1,794.62

11 $9,000.00 $400.00 $9,400.00 $10,794.62 $863.57 $11,658.19 $2,258.19

12 $9,400.00 $400.00 $9,800.00 $11,658.19 $932.66 $12,590.85 $2,790.85

13 $9,800.00 $400.00 $10,200.00 $12,590.85 $1,007.27 $13,598.12 $3,398.12

14 $10,200.00 $400.00 $10,600.00 $13,598.12 $1,087.85 $14,685.97 $4,085.97

15 $10,600.00 $400.00 $11,000.00 $14,685.97 $1,174.88 $15,860.85 $4,860.85

16 $11,000.00 $400.00 $11,400.00 $15,860.85 $1,268.87 $17,129.71 $5,729.71

17 $11,400.00 $400.00 $11,800.00 $17,129.71 $1,370.38 $18,500.09 $6,700.09

18 $11,800.00 $400.00 $12,200.00 $18,500.09 $1,480.01 $19,980.10 $7,780.10

19 $12,200.00 $400.00 $12,600.00 $19,980.10 $1,598.41 $21,578.51 $8,978.51