Final answer:
The present value of Derek's $15,000 gift in today's dollars, assuming a 5.5% compounded annual interest rate and a 10-year period until he receives it, is approximately $8,773.94. We use the formula for calculating the present value of a future sum with compound interest to arrive at this figure.
Step-by-step explanation:
The question involves finding the present value of a future sum of money ($15,000) using the formula for compound interest. Derek will receive this sum in 10 years, and it is assumed that he can earn a 5.5% annual compounded rate of return.
To calculate the present value (PV) of the future sum, we use the formula:
PV = FV / (1 + r)^n
Where:
- FV is the future value of the money,
- r is the annual interest rate (as a decimal), and
- n is the number of years until the amount is received.
Applying the values we have:
PV = $15,000 / (1 + 0.055)^10
Calculating that gives us:
PV = $15,000 / (1.055)^10
PV = $15,000 / 1.7086871
PV ≈ $8,773.94
Therefore, the present value of Derek's gift in today's dollars is approximately $8,773.94, making option b the right answer.