Sally has just won the lottery.She is given two equivalent choices as to how the winnings will be paid.She can receive a lump sum of $A today or she can receive 20 semi-annual payments.The first payment would be $10,000 and is to be paid today,with each succeeding payment being 91% of the preceding payment [2^nd payment = 10,000(0.91)].If the interest rate is j₂ = 8%,what is the value of A?

Question

Quizplus · Accepted Answer

We can use the present value formula to compare the two choices:

PV of lump sum = A
PV of semi-annual payments = 10,000 + (10,000)(0.91)/(1+0.04)^1 + (10,000)(0.91)^2/(1+0.04)^2 + ... + (10,000)(0.91)^19/(1+0.04)^19

where we use a semi-annual interest rate of 4% (half of the annual rate of 8%).

Using a financial calculator or spreadsheet, we find that the present value of the semi-annual payments is $74,463.30. Therefore, the better choice is to take the lump sum of $74,463.30 today instead of the semi-annual payments.

Sally Has Just Won the Lottery