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 4% annually, which alternative she should take? and why? Select one: O a. She should take the annuities because they are $112,718 higher in value than the single amount O b. She should take the annuities because they are $139,311 higher in value than the single amount c. 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 O d. She should take the annuities because they are $132,380 higher in value than the single amount

Answer 1

Answer-

Amount of lottery won = $ 1000000

First Option of getting a single amount = $ 500000 paid immediately

Second Option $ 40000 at the end of each year

PMT = $ 40000
Number of years = 26
Future value = $ 0
Discount rate = YTM = I/Y = 4 % annually
Present value = PV = ?

Present Value = PV = $ 639310.77

The Second Option is higher than first Option = $ 639310.77 - $ 500000

The Second Option is higher than first Option = $ 139310.77
The Second Option is higher than first Option = $ 139311

The Correct Option is b.
Dana should take annuities a the amount is higher than $ 139311 in value than accepting single amount