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.