You would like to buy a new car. You have $50 000 or so, but the car costs

$68 500. If you can earn 9 per cent, how much do you have to invest today to buy the car in two years? Do you have enough? Assume the price will stay the same.

What we need to know is the present value of $68 500 to be paid in two years, assuming a 9 per cent rate. Based on our discussion, this is:

PV = $68 500/1.092 = $68 500/1.1881 = $57 655.08 You are still about $7 655 short, even if you are willing to wait two years.

As you have probably recognised by now, calculating present values is quite similar to calculating future values, and the general result looks much the same.

The present value of $1 to be received t periods into the future at a discount rate of r is:

PV = $1 × [1/(1 + r)t] = $1/(1 + r)t [5.2]