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???
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)