Question

g Congratulations, you've just won the $2,200,000 state lottery! The lottery commission offers you the choice of $98,000 per year for 30 years or a one-time, lump-sum payment of $880,000 If your intensions are to save all of the lottery winnings (regardless of annual cash flow or lump-sum) for retirement in an account that earns 3.00% annually, which payment option should you choose

Answer 1

the choice of $98,000 per year for 30 years

Step-by-step explanation:

To determine the option i would prefer, i have to find the present value of fiest opotion and compare it with the value of the second option.

To find the present value of the first option, the future value has to be determined first.

The formula for determining the future value of an annuity is :

The formula for calculating future value = A (B / r)

A = amount

B = annuity factor

r = interest rate

Annuity factor = {[(1+r)^n] - 1} / r

n = number of years

$98,000 x[ (1.03)^30 - 1 ] / 0.03 = $4,662,390.74

Now we determine the present value

PV = FV x ( 1+r)^-n

$4,662,390.74 x (1.03)^-30 = $1920,843.25

The payoff of the first option is greater than that of the second so i would choose the first