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.

the correct answer would be b, when, queen, calder hall and london.

explanation:

we always capitalize words when a paragraph or sentence is starting, when an important name is used, when a place is being written, or simply when a noun is used, etc. so in this sentence, sentence is starting from 'when', so it will be written in capital letters. secondly, queen is considered to be an important person, so it will also be written in capital letter. next, the name of the town is mentioned, i-e calder hall, which will also be written in capital letters. in the last,   city name is being used, 'london', which will also be written in capital letters. so option b is the most appropriate one.