Question

Suppose you win a lottery. You have two choices for receiving the money. Choice 1: $50 000 at the end of each year for 20 years Choice 2: $500,000 now If current interest rates are approximately 8% p.a. compounded yearly, which is the better choice. Justify your answer with a clear solution and explanation.

Answer 1

The first option of an annuity is better because the amount is worth $2,288,098 in today's cash

Step-by-step explanation:

The better choice would be the option with the higher present value discounted at the required rate of return. The required rate of return is 8%.

To determine the better choice, we would compare the present value of choice 1 to the $500, 000 receivable today under choice 2

The present value of $50 000 at the end of each year for 20 years is

PV = A × ((1+r)^n - 1)/r

r- 8%, n - 20, A= 50,000, PV - Present value

PV = 50,000 × ( ( 1.08)^(20) - 1) /0.08

= 50,000 × 45.7619643

= $2,288,098

The first option of an annuity is better because the amount is worth $2,288,098 in today's cash which is higher than $500,000 offered by the second option.

The first option is greater than the second by $1,788,098.21 i.e

$2,288,098 - $500,000