| Time Value of Money |
Invested money earns interest (if in a bank account, for example)
or some rate of return (if invested in something else |
| Compound interest |
Any money earned on the investment (interest or other income) is
immediately reinvested at the same rate of return (interest) as the original investment.
Therefore: Interest is also earned on the reinvested earnings. |
| Interest rate, rate of return,
discount rate, effective rate |
For the purpose of present value analysis they are the same.
From now on, only the term interest will be used. |
| Future value |
The value of an investment after a designated period of time, given
a specific interest rate. |
| Example |
$100 invested at 10% for three years,
interest is compounded (calculated) annually:
|
Investment |
interest
|
interest
|
|
|
rate |
earned |
year
1 |
100 |
10% |
10 |
year
2 |
110 |
10% |
11 |
year
3 |
121 |
10% |
12.1 |
Value
of investment |
|
|
|
after
three years: |
133.1 |
|
|
|
|
This is an example of Future Value. It can also be determined by
using the compound interest formula (future value formula): |
| Compound interest formula or future
value formula |
(1+r) |
n |
Where r = interest rate per compounding period |
|
|
and n = the number of compounding periods. |
(1+.1) |
3 |
equals |
1.331 |
|
|
|
| Interest can be compounded annually, semi-annually,
quarterly, even daily. However, if you are told that you can earn 10% on an
investment and that interest will be compounded semi-annually, that does not mean that you
will earn 10% twice a year on your investment. Instead you will earn 5% twice a
year. If interest were compounded quarterly, you would earn 2.5% four times a year,
etc. In other words, If there is more than one compounding period per year the
interest rate (r or i) is divided by the number of compounding periods per year. The
number of years are multiplied by the number of compounding periods per year, resulting in
a properly adjusted value for (n) For example |
| 10%, 3 years, semi-annual compounding: |
|
| 10%, 3 years, quarterly compounding: |
|
| Future Value Formula: |
this is written as follows: FV(r,n): in the above case: FV
(10%, 3) = 1.331 |
| The example above can now
be expressed as follows: |
If $100 are invested at 10%, compounded annually, for three
years, how much will the investment be worth at the end of three years? |
| In equation form: |
100 x
FV(10%,3) = X |
100 x 1.331 =
X |
$ 133.10 = X |
|