Question

Suppose you win a small lottery and you are given the following choice: You can receive (1)an immediate payment of $10,000 or (2)two annual payments,each in the amount of $5,200,with the first payment coming one year from now,and the second payment coming two years from now.You would choose to take the immediate payment of $10,000 if the interest rate is:________.

A) 2 percent,but not if the interest rate is 1 percent.
B) 3 percent,but not if the interest rate is 2 percent.
C) 4 percent,but not if the interest rate is 3 percent.
D) 5 percent,but not if the interest rate is 4 percent.

Answer 1

Answer: B) 3 percent, but not if the interest rate is 2 percent.

Step-by-step explanation:

Assuming the interest rate is 1%, the present value of the two year payments is;

= (5,200 / ( 1 + 1%)) + (5,200 / ( 1 + 1%)²)

= $10,246.05

Assuming rate is 2%.

= (5,200 / ( 1 + 2%)) + (5,200 / ( 1 + 2%)²)

= $10,096.12

Assuming rate is 3%

= (5,200 / ( 1 + 3%)) + (5,200 / ( 1 + 3%)²)

= $9,950.04

At 3%, the present value of the annual payment is less than the value you could be paid today so you would take the $10,000 instead.

At 2% however, the present value of the annual payments is more than the value you could collect today so you would not take the $10,000.