Compound Interest
Investing for retirement usually consists of putting money into an account
and letting its value grow until the investor reaches retirement age.
The interest earned on the investment each year is left in the account
so that future interest growth will be applied to interest from prior
years. This process of getting interest on interest is called compounded
interest.
Over the short term compound interest is not that exciting. But over
long periods of time, such as 3040 years compound interest enable
investments to grow significantly. For example, $1000 invested at
5% and left to grow for 40 years will be worth over $7000.
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Compound Interest
If you put $1000 in the bank and draw 5% interest, then at the end of the
year you will have $1050. If you leave the entire amount in the bank
for another year you will then have $1103. In the second year, not
only did you get interest on the original investment, but you also got
interest on the interest you earned the prior year. This is called
compounded interest  interest applied to interest.
Compound interest is of most importance to investors who are able to leave
their investment to grow over long periods of time. The $1000 investment
mentioned above, when invested for 40 years at 5%, will be worth over $7000!
It's only when interest is compounded over longer periods of time that the
effects of compound interest are obvious. The following 40 year investment
chart shows how the future value of an investment grows most spectacularly
in the later years. In this example, half of the future value is earned in the last 10
years.
This is exactly why retirement planning calls for early investments  to put
money into account that can work for 3040 to achieve the full advantage of
compound interest.
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Interest Rate
The sensitivity of the future value of an investment to small changes in interest
rates may not be obvious to beginning investors.
At first glance it might be tempting to say that the difference between
investing at 5% and 6% would not be significant. However, as the next
table points out, an increase of a single percentage point on an investment
results in a 50% increase in the future value of an investment.
This next table shows the future value (in 5 year intervals) of a $1000
investment over 20 and 40 years at various interest rates from 4% to 10%.
Interest Rate  Future Value (20 years)  Future Value (40 years)


4%  $2222  $4,801
 5%  $2712  $7,040
 6%  $3310  $10,286
 7%  $4038  $14,974
 8%  $4926  $21,725
 9%  $6009  $31,409
 10%  $7328  $45,259

The table shows that an increase of a single percentage point results in an almost
50% increase in the future value of the investment. This is why retirement planning
is so sensitive to interest rates and why investors work hard to improve their
rate of return by even a single percentage point!
The table also points out how interest rates and time of investment work together.
A one percentage point investment improvement, after 20 years, would result in
a 25% increase in future value of the investment. However, after 40 years that
same one percentage point improvement will grow the original investment by 50%.
Retirement planning must start early for compound interest to work best, and every
percentage point of interest is critical!
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Interval
The frequency at which interest is applied to an investment account can be important
to a retirement planner.
When a company, such as a bank, advertises an interest rate they also disclose how
often interest will be added to the account. It was common for many years for banks
to compound interest quarterly  that is, every 3 months they would look at the balance
of the account and add interest to the balance, at onefourth their advertised annual
rate.
Today is it possible to invest money which compounds interest monthly, daily, or even
continuously.
For most retirement planning a yearly compounded interest is assumed. It is the most
conservative way to estimate future income.
The following table compares the effect of compounding interest monthly, quarterly,
and yearly. The table is for a $1000 investment over 40 years.
Interest Rate  Yearly  Quarterly  Monthly


5%  $7,040  $7,298  $7,358
 10%  $45,259  $51,978  $53,700

At 5%, interest compounded monthly results in a 5% increase in future value as
compared to interest compounded yearly.
However at 10%, interest compounded monthly results in an 18% increase in future
value!
The bottom line is that investors can benefit significantly from interest rates
which are compounded more frequently.
