Question

You just won the lottery and the lottery commission will either give you $6 million as a lump sum, or 20 equal, annual payments of $500,000. Assume an interest rate of 6% per year, compounded annually. What should you do

Answer 1

Answer:

I should receive annual payments of $500,000

Explanation:

Lump sum amount = $500,000

or

Annual Payment = $500,000

Interest rate = 6%

Payment of fix amount for a specified period is known as annuity. Present value of annuity will be compared to lump sum amount.

PV of annuity = P [ ( 1 - ( 1 + r )^-n ) / r ]

PV of annuity = $500,000 [ ( 1 - ( 1 + 0.06 )^-20 ) / 0.06 ]

PV of annuity = $500,000 [ ( 1 - ( 1.06 )^-20 ) / 0.06 ]

PV of annuity = $5,734,961

Annual payment will provide extra benefit of $734,961 than lump sum payment.