You have just won the lottery! you may take your winnings in either a single immediate payment of $1,000,000 or in annual payments of $25,000 forever. at what interest rate would you be indifferent between these two choices? [hint: a + a^2 + a^3 + … = a/(1-a), a< 1, where a=1/(1+r); or pv=m/r]

The interest rate of 2.5% per year will make the two choices indifferent.

Explanation:

Please find the explanations and calculation as below:

The interest rate that makes the two choices indifferent is the interest rate at which the present value of the annual perpetuity of $25,000 will be equal to the immediate payment of $1,000,000.

Let us denote r is the interest rate needed to be found.

As a result, we have: $25,000 / r = $1,000,000 <=> r = $25,000/$1,000,000 = 2.5%.

Thus, at 2.5% per year interest rate, it will be indifferent between these two choices.