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

## Question:

You have won a contest and will receive $2,500 a year in real terms for the next 3 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 6.3 percent and the inflation rate is 3.1 percent. What are your winnings worth today?

## Present Value of Annuity:

An annuity is a streak of payments or deposits occurring for a certain time horizon at equal intervals. The present worth of an annuity is predominantly governed by the relevant interest rate.

## Answer and Explanation: 1

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

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Chapter 8 / Lesson 3Learn how to find present value of annuity using the formula and see its derivation. Study its examples and see a difference between Ordinary Annuity and Annuity Due.