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Congratulations! You have just won the lottery! However, the lottery bureau has just informed you that you can take your winnings in one of two ways. Choice X pays $1,000,000. Choice Y pays $1,750,000 at the end of five years from now. Using a discount rate of 5 percent, based on present values, which would you choose? Using the same discount rate of 5 percent, based on future values, which would you choose? What do your results suggest as a general rule for approaching such problems?

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Final answer:

To determine which choice is more beneficial, we need to calculate their present values and future values using a discount rate of 5 percent. Based on these calculations, we would choose choice Y if considering present values and choice X if considering future values. A general rule for approaching such problems is that if the discount rate is higher than the growth rate, it is better to take the payment sooner (choice X). Conversely, if the discount rate is lower than the growth rate, it is better to defer the payment (choice Y).

Step-by-step explanation:

To determine which choice is more beneficial, we need to calculate their present values and future values using a discount rate of 5 percent. For choice X, the present value is $1,000,000 because it is received immediately. For choice Y, we need to calculate the present value of $1,750,000 received after five years. Using the present value formula, the present value of choice Y is approximately $1,381,012.

For future values, we apply the discount rate to calculate the value of choice X after five years. Using the future value formula, the future value of $1,000,000 after five years is approximately $1,276,282. The future value of choice Y remains $1,750,000 as it is already five years in the future.

Based on these calculations, we would choose choice Y if considering present values and choice X if considering future values.

A general rule for approaching such problems is that if the discount rate is higher than the growth rate, it is better to take the payment sooner (choice X). Conversely, if the discount rate is lower than the growth rate, it is better to defer the payment (choice Y).

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