Future Value...
I will now give you two choices: you can have $1000 now or
you can have $100 a year for ten years. Which would you choose?
I think your intuition already tells you to take the first choice, but
let’s look at this from a more technical perspective. Let’s assume
that you can put this money into a bank account that pays 5% interest
compounded annually. The table below shows how much interest you can
earn with such an investment.
|
Year |
Cash Added |
Start of Year |
Interest Earned |
End of Year |
|
1 |
1000.00 |
1000.00 |
50.00 |
1050.00 |
|
2 |
0.00 |
1050.00 |
52.50 |
1102.50 |
|
3 |
0.00 |
1102.50 |
55.13 |
1157.63 |
|
4 |
0.00 |
1157.63 |
57.88 |
1215.51 |
|
5 |
0.00 |
1215.51 |
60.78 |
1276.28 |
|
6 |
0.00 |
1276.28 |
63.81 |
1340.10 |
|
7 |
0.00 |
1340.10 |
67.00 |
1407.10 |
|
8 |
0.00 |
1407.10 |
70.36 |
1477.46 |
|
9 |
0.00 |
1477.46 |
73.87 |
1551.33 |
|
10 |
0.00 |
1551.33 |
77.57 |
1628.89 |
Table 1. $1000 invested in Year 1 at
5%.
At the end of ten years (if you put
this money in a bank account that pays 5% interest), your $1000
investment in the first year would become $1628! The $1628 would be
called the future value of that particular investment.
Let’s do a similar future value table for the second choice: earning
$100 a year for ten years. The table below shows the calculations:
|
Year |
Cash Added |
Start of
Year |
Interest Earned |
End of Year |
|
1 |
100.00 |
100.00 |
5.00 |
105.00 |
|
2 |
100.00 |
205.00 |
10.25 |
215.25 |
|
3 |
100.00 |
315.25 |
15.76 |
331.01 |
|
4 |
100.00 |
431.01 |
21.55 |
452.56 |
|
5 |
100.00 |
552.56 |
27.63 |
580.19 |
|
6 |
100.00 |
680.19 |
34.01 |
714.20 |
|
7 |
100.00 |
814.20 |
40.71 |
854.91 |
|
8 |
100.00 |
954.91 |
47.75 |
1002.66 |
|
9 |
100.00 |
1102.66 |
55.13 |
1157.79 |
|
10 |
100.00 |
1257.79 |
62.89 |
1320.68 |
Table 2. $100 invested per year for 10 years at 5%.
The future value of $1320 of this investment is $398 less than
having the $1000 in the first year. This exercise clearly shows the
superiority of the first choice.
But suppose you are offered these two choices: getting $800 in the
first year or getting $100 a year for ten years. The second choice
offers more money, but the first choice has you earning more interest
revenue. Now your intuition probably really can’t tell you which is
the better choice. So we calculate a future value for receiving the
$800 in the first year:
|
Year |
Cash Added |
Start of Year |
Interest Earned |
End of Year |
|
1 |
800.00 |
800.00 |
40.00 |
840.00 |
|
2 |
0.00 |
840.00 |
42.00 |
882.00 |
|
3 |
0.00 |
882.00 |
44.10 |
926.10 |
|
4 |
0.00 |
926.10 |
46.31 |
972.41 |
|
5 |
0.00 |
972.41 |
48.62 |
1021.03 |
|
6 |
0.00 |
1021.03 |
51.05 |
1072.08 |
|
7 |
0.00 |
1072.08 |
53.60 |
1125.68 |
|
8 |
0.00 |
1125.68 |
56.28 |
1181.96 |
|
9 |
0.00 |
1181.96 |
59.10 |
1241.06 |
|
10 |
0.00 |
1241.06 |
62.05 |
1303.12 |
Table 3. $800 invested in Year 1 for 10 years at 5%.
Now the two investments are pretty close, but having $100 a year for
ten years (FV = $1320) is slightly superior to having $800 ($1303) in
the first year.
You can do similar simulations for many scenarios. For example, which
is better:
- $800 in the first year or $100 a year for ten years at 3%?
- $800 in the first year or $100 a year for ten years at 7%?
- $200 a year for four years or $100 a year for ten years at
10%?
- $500 for two years or $350 for three years at 2%, both for a
ten-year period?
- $900 in the first year at 7% and $800 in the first year at
8%, both for a ten-year period?
- $900 in the first year at 7% and $800 in the first year at
8%, both for a twenty-year period?
In each of these cases, you are using the future value financial
technique to tell you which of the two investments is the better
investment. |
