Question

Suppose you win a small lottery and have the choice of two ways to be paid: You can accept the money in a lump sum or in a series of payments over time. If you pick the lump sum, you get $3,103 today. If you pick payments over time, you get three payments: $1,100 today, $1,100 1 year from today, and $1,100 2 years from today.

At what interest rate would you consider either choice to be equal? (Write your answer as a percentage, and round to the nearest first digit. E.g., if your answer is 2.5%, you should write in your answer as 2.5)

Answer 1

Option 1 : PV = 3103

Option 2: PV = 1100 + 1100/(1 + r) + 1100/(1 + r)2

where r = interest rate

Equating both PV:

3103 = 1100 + 1100/(1 + r) + 1100/(1 + r)2

r = 6.49%