Final answer:
To be indifferent between $812 today or $X in 6 years at a 7% interest rate, $X would need to be the future value of $812 compounded at 7% over 6 years, which is approximately $1219.77.
Step-by-step explanation:
When deciding between receiving $812 today or a different amount $X in 6 years, given a 7% interest rate, we can rely on the concept of the time value of money. To be indifferent between the two options, the value in the future needs to be equivalent to the present value when considering the specified interest rate. This is calculated using the formula for future value: Present Value (PV) × (1 + interest rate)^number of periods.
To find the value of $X that makes you indifferent, you can set up the equation as follows:
- Calculate the future value based on the present value of $812, the annual interest rate of 7% (0.07), and the time period of 6 years.
- Formula: $X = $812 × (1 + 0.07)^6.
Using this formula, we can calculate the future value as follows:
$X = $812 × (1 + 0.07)^6 = $812 × (1.07)^6 = $812 × 1.5007 ≈ $1219.77.
Therefore, you would be indifferent between receiving $812 today or approximately $1219.77 in 6 years at a 7% interest rate.