You just signed a business consulting contract with one of your clients. The client will pay you $50,000 a year for five years for the service you will provide over this period. You anticipate the general inflation rate over this period to be 6%. If your desired inflation-free interest rate (real interest rate) is to be 4%, what is the worth of the fifth payment in present dollars

The present value of the fifth payment is $30710.

Explanation:

The rate of interest must include the effect of inflation which can be found by the fisher formula:

(1+i) = (1+r) * (1+f)

After putting values we have:

(1+i) = (1+.04) * (1+.06) = 1.1024

This implies

i = 10.24%

So the present value of fifth year inflow is:

Present Value = $50,000 * discount factor at 5 years time

= $50,000 * 1 / (1 + 0.1024) ^5 = $50,000 * 0.614 = $30710

So the present value of the fifth payment that is receivable in five years time is worth $30710 in todays value.