Question

Dana just won $1,000,000 in the state lottery. Her prize can be taken either in the form of $40,000 at the end of each of the next 26 years (annuities), or as a single amount of $500,000 paid immediately. If the discount rate is 3% annually, which alternative she should take? and why?

Select one:

a. She should take the $500,000 because it's value today is higher than the value of the $40,000 payments for the next 26 years

b. She should take the annuities because they are $215,074 higher in value today than the single amount

c. She should take the annuities because they are $233,214 higher in value today than the single amount

d. She should take the annuities because they are $208,178 higher in value today than the single amount

Answer 1

We can calculate this type of questions by using Present value concept.

We should compute & compare present value of Both options.

Present value of Single amount = $ 500,000

Present value of annuities = Payment * PVAF(3%,26 years)

Present value of annuities = 40,000 * [ 1 - ( 1 / (1.03)26 ] / 0.03

Present value of Annuities = 40,000 * 17.8768424

Present value of Annuities = $ 715,073.697

Diffence between the present value of both options = $ 715,073.697 - 500,000 = $ 215,073.697

Diffence between the present value of both options = $ 215,074

Option b is correct.

She should take annuties because they are $215,074 higher in value today than the single amount.

Remaining options are incorrect.

Option B is correct.