Final answer:
The present value of $1,200 to be received in 15 years with an 8 percent opportunity cost is approximately $378.35, calculated using the formula PV = FV / (1 + r)^n.
Step-by-step explanation:
The present value of an amount of money to be received in the future is its worth in today's dollars, given a certain interest rate, also known as the opportunity cost. The formula to calculate the present value (PV) is: PV = FV / (1 + r)^n where FV is the future value, r is the interest rate (as a decimal), and n is the number of periods until the payment will be received.
To calculate the present value of $1,200 to be received 15 years from today at an opportunity cost of 8 percent, we use the formula mentioned above. Thus, the present value is:
PV = $1,200 / (1 + 0.08)^15
Now calculate the denominators value, which is (1 + 0.08)^15, and then divide $1,200 by this number to get the present value. Let's complete the calculation:
(1 + 0.08)^15 = 1 + r)^n = (1.08)^15
Once calculated, this figure is approximately 3.1722.
PV = $1,200 / 3.1722 ≈ $378.35
The present value of $1,200 to be received 15 years from now, using an discount rate of 8 percent, is approximately $378.35.