Congratulations! You have just won the lottery ,which will pay you an annuity of $50,000 per year for the rest of your life. If you are 21 today and will die with certainty at 90, this means you will receive 70 payments of $50,000. Let’s say someone offers to give you $1,000,000 today in exchange for this annuity. If the interest rate is 5%, should you take this deal? Why or why not?
To compare the two alternatives, we need to calculate the present worth of the two options.
The present worth of Option 2 is given in the question ($1,000,000)
Calculation of the present worth of Option 1 (Annuity):
=P*[1-(1+r)^-n]/r,
where
P=Periodic payment,
r=rate per period
n=number of periods.
Therefore,
=$50,000*[{1-(1+0.05)^-70}/0.05]
=$50,000*[{1-(1.05)^-70}/0.05]
=$50,000*[{1-0.03287}/0.05]
=$50,000*[{0.96713}/0.05]
=$50,000*19.34
=$967,130 (apprx)
Hence, I should opt for Option 2 as it has a higher present worth($1,000,000) as compared to Option 2 ($967,130).
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