Question

You will receive $5,000 a year in real terms for the next 5 years. Each payment will be received at the end of the period with the first payment occurring one year from today. The relevant nominal discount rate is 10.725 percent and the inflation rate is 3 percent. What are your winnings worth today in real dollars?

Answer 1

Answer:

$20,229.5

Explanation:

Given:

Amount to be received = $5,000

Time period, n = 5 years

nominal discount rate = 10.725%

inflation rate = 3 percent

Now,

Using the Fischer's relation, we have

1 + Nominal rate = ( 1 + Real rate ) × ( 1 + Inflation )

on substituting the values, we get

( 1 + 10.725% ) = ( 1 + Real rate ) × ( 1 + 3% )

or

1.10725 = ( 1 + Real rate ) × 1.03

or

( 1 + Real rate ) = 1.075

or

Real rate = 1.075 - 1 = 0.075 or 7.5%

Thus,

Present Value of an ordinary annuity that makes $5000 every year payment for 5 years will be calculates as:

Present value = Monthly payment × $[\frac{(1-(1+r^{-n})}{r}]$

or

Present value =$5000\times[\frac{1 - (1 + 0.075)^{-5}}{0.075}]$

or

Present value = 5000 × 4.0459

or

Present value = $20,229.5