Question

Steve McNamara won the power ball in Missouri! He has the option of receiving a check right now for $125,000 or receiving a check for $50,000 each year for three years. Steve would receive the first check for $50,000 immediately. At what interest rate would Steve have to invest his winning for him to be indifferent as to how he receives his wining?

Answer 1

For Steve to be indifferent between how he receives his wining, the present value of three checks should be $125,000 which is the present value of the option of receiving a check right now. hence we have

125000 = 50000 + 50000(1 + i%)^-1 + 50000(1 + i%)^-2

-125000 + 50000(1 + (1 + i%)^-1 +(1 + i%)^-2) = 0

For i = 21%, this value is -472.99 and for i = 22%, this value is -423.37

Find the rate of interest = 21% + (22% - 21%)*(472.99/(472.99 + 423.27))

= 21.52%

Hence the rate of interest is 21.52%.