# Math Help - Setting a fair price

1. ## Setting a fair price

You have a contract that entitles you to receive $1 million 20 years from now. But you can't wait and want your money now. You want to sell your contract. What is a fair price for it? Assume the risk-free, inflation adjusted interest rate is 3% per year, compounded continuously. For this question, do I just calculate the total amount and take 3% off for 20 years or how do I do it??? what is the most efficient or precise way of making an equation and solve??? 2. Originally Posted by mathsohard You have a contract that entitles you to receive$1 million 20 years from now. But you can't wait and want your money now. You want to sell your contract. What is a fair price for it? Assume the risk-free, inflation adjusted interest rate is 3% per year, compounded continuously.

For this question, do I just calculate the total amount and take 3% off for 20 years or how do I do it??? what is the most efficient or precise way of making an equation and solve???
Present Value of the annuity.

3. I am not really sure what Value of the annuity is ....???

4. Originally Posted by mathsohard
I am not really sure what Value of the annuity is ....???
$\displaystyle\text{PV}=\frac{\text{FV}}{(1+i)^n}$

5. Compounding continuously has different formula:
(e = Euler number)
P = F / e^(rt) = 1000000 / 2.71828...^(.03*20) = 517281.85797...

6. so P = F / e^(rt) is this the one I am supposed to use???

7. Aye, aye, Captain

8. Where did you see an annuity here? All I see is a one-off payment of $1 million in 20 years' time. (Annuity is a series of annual payments). So, to sum up, because money has 'time value' ($1 today is worth more to us than $1 20 years from now), you need to apply a discount factor to the amount that you will receive in 20 years' time, to bring it to a today's value ('fair price' in your question). The formula by Wilmer makes this adjustment, where 1/(e^rt) is the discount factor. By multiplying your$1 million by that discount factor, you bring it to the terms of "today's money".

r- interest rate per time period (3% pa in your case)
t - number of time periods (20 years in your case)

9. Originally Posted by Volga
Where did you see an annuity here?

r- interest rate per time period (3% pa in your case)
t - number of time periods (20 years in your case)
No annuity; dwsmith changed to FV later...

PV = 1000000 / 1.03^20 is IF interest compounds annually only.