## 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.