The time value of money
1. The dollar and time
Look at the following data:
| Year | 1963 | 2009 |
|---|---|---|
| New honours graduate salary | $800 per year | $50,000 per year |
| 3 bedroom house | $2,825 | $400,000 |
| Small car | $400 | $10,000 |
All monies are in dollars, but they clearly do not have the same value. The $ in 1963 was worth more than the one today. So a $ today is worth more than a $ tomorrow; a demonstration of the time value of money.
This approach is general, not specific or numerate. That is where discount tables come in.
2. Discount tables
Imagine that you invest $100 at 10% per annum, compounded annually. Your deposit would grow.
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Value | 100 | 110 | 121 | 133 | 146 | 160 | 176 |
This is the future value of a $ today at 10%. We can turn this round and look at the present value of a $ earned in the future. It is the reciprocal of the numbers above.
Present value of $1 earned in the future.
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Present value | 1.000 | 0.909 | 0.826 | 0.75 | 0.684 | 0.625 | 0.568 |
This tells us that a $ received in 3 years time is worth the same as 75 cents today at 10% rate of interest.
Do the same thing for an interest rate of 20% and we get:
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Future value | 100 | 120 | 144 | 173 | 207 | 249 | 299 |
| Present value | 1.000 | 0.833 | 0.694 | 0.578 | 0.483 | 0.401 | 0.334 |
The higher the interest rate, the less money is worth received in the future.
For interest rate, read discount rate and you have the discount tables.
