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Emilio offers you two options: $456 today or in 11 years. Suppose that you are not risk averse. If the interest rate is 10

percent, then at what value of X would you be indifferent between the two options? Round your answer to the nearest two
decimal place.

1 Answer

3 votes

Final answer:

The value of X at which one would be indifferent between receiving $456 today or in 11 years at a 10% interest rate is the present value of $456, which is approximately $173.55 when rounded to the nearest two decimal places.

Step-by-step explanation:

To determine the value of X at which you would be indifferent between receiving $456 today and receiving it in 11 years at an interest rate of 10%, you need to calculate the present value of the future amount. This is done using the formula for present value, which is:

Present Value = Future Value / (1 + interest rate)number of periods

In this case, the future value is $456, the interest rate is 10% (or 0.10 as a decimal), and the number of periods is 11 years. Using the formula, we get:

Present Value = $456 / (1 + 0.10)11

After performing the calculation, the present value of $456 is approximately $173.55. This means that if offered $173.55 today at 10% interest rate compounded annually, you would have $456 in 11 years, making you indifferent between the two options.

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