You have won a contest and will receive $2,500 a year in real terms for the next 3 years. Each...

The calculated present worth of the winnings is $7,044.42

The real discount rate is given by:

{eq}\begin{align*} &= \text{Nominal discount rate - inflation rate} \\[0.3 cm] &= 6.3\% - 3.1\% \\[0.3 cm] &= 3.2\% \end{align*} {/eq}

The present worth of the annual payments is given by:

{eq}P\, = \dfrac{1\, -\, \left ( 1\, +\, i \right )^{-n}}{i}\times R {/eq}

Where;

R = annual payment in real terms = $2,500

i = real interest rate = 3.2%

P = Present value

n = number of years = 3

{eq}P\, = \dfrac{1\, -\, \left ( 1\, +\, 0.032 \right )^{-3}}{0.032}\times 2,500 {/eq}

P = $7,044.42