Question

Jessica has just won a game organized by her community. As a reward, she needs to choose among three options: (A) She can choose to receive a lump-sum today of $55, (B) to receive 10 end-of-year payments of $9, or (C) to receive 30 end-of-year payments of $5. If we assume that she can earn 6% annually, which option should she choose?

Answer 1

Interest Rate = 6%

Option 1:

Lump sum today of $55

Present Value = $55

Option 2:

$9 end of the year payments for 10 years

Present Value = $9/1.06 + $9/1.06^2 + ... + $9/1.06^10
Present Value = $9 * (1 - (1/1.06)^10) / 0.06
Present Value = $66

Option 3:

$5 end of the year payments for 30 years

Present Value = $5/1.06 + $5/1.06^2 + ... + $5/1.06^30
Present Value = $5 * (1 - (1/1.06)^30) / 0.06
Present Value = $69

So, Jessica should choose Option 3 as its present value is maximum.