Question

Juan just won $2.5 million in the state lottery. He is given the option of receiving a total of $1.3 million now, or he can elect to be paid $100,000 at the end of each of the next 25 years. If Juan can earn 5% annually on his investments, from a strict economic point of view, which option should he take? Explain why.

Answer 1

The question is based on selection of option that will be beneficial for Juan.

There are two options -One receiving money now and other is receiving money on yearly basis.

We have to compare both option at equal time.It means either we calculate present value of annual amount and compare with today's amount.

Similarly, we can find future value of both amount at the end of 25 years.

Here we evaluate option on the basis of present value method

Present Value of Receiving money now

=

$       13,00,000

Present Value of Yearly amount

=

Yearly amount x Present value of annuity of $ 1

=

$          1,00,000

x

14.094

=

$       14,09,394

Working:

Present value of Annuity of $ 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.05)^-25)/0.05

i

5%

=

14.094

n

25

Based on above calculation , we can see that present value of receiving amount annually has higher Present value.

So, he should take option of receiving money Annually.