Final answer:
To select the prize with the largest present value, we need to calculate the present value of each option. Option (d) has the largest present value of $1043.95. Therefore, you should choose the annuity of 5 yearly payments of $250 with the first payment made immediately.
Step-by-step explanation:
In order to select the prize with the largest present value, we need to calculate the present value (PV) of each option. Option (a) is a perpetuity of $100 per year, starting one year from now. The present value of a perpetuity can be calculated using the formula PV = Cash Flow / Interest Rate.
So, for option (a), the present value would be $100 / 0.10 (0.10 = 10% expressed as a decimal) = $1000. Option (b) is an annuity of 5 yearly payments of $250, with the first payment made one year from now. The present value of an annuity can be calculated using the formula PV = Cash Flow * (1 - (1 + Interest Rate)^(-Number of Periods)) / Interest Rate. So, for option (b), the present value would be $250 * (1 - (1 + 0.10)^(-5)) / 0.10 = $1043.95. Option (c) is a perpetuity of $100, with the first payment made immediately.
The present value of option (c) would be $100 / 0.10 = $1000. Option (d) is an annuity of 5 yearly payments of $250, with the first payment made immediately. The present value of option (d) would be $250 * (1 - (1 + 0.10)^(-4)) / 0.10 + $250 = $1043.95.
Comparing the present values, option (d) has the largest present value of $1043.95. Therefore, if you want to select the prize with the largest present value, you would choose option (d): an annuity of 5 yearly payments of $250 with the first payment made immediately.