Final answer:
After calculating the present value of $21,600, discounted at an annual rate of 17% over 30 years, it is approximately $1,238.69. Since this present value is greater than $200 today, the better financial choice is to choose the $21,600 in 30 years.
Step-by-step explanation:
The problem presented is a question of time value of money, which is a concept in finance. Specifically, it relates to calculating the present value of a future sum of money by discounting it with a given interest rate. The student is asked to decide between receiving $21,600 in 30 years or $200 today, with a discount rate of 17%.
To resolve the problem, we must calculate the present value of $21,600 discounted back 30 years at the rate of 17%. The formula for present value (PV) is:
PV = FV / (1 + r)^n
where:
- FV = Future Value, which is $21,600
- r = annual discount rate, which is 0.17
- n = number of years, which is 30
Using the formula, we can calculate:
PV = $21,600 / (1 + 0.17)^30
PV = $21,600 / (1.17)^30
PV = $21,600 / 17.449
PV = $1,238.69 (approximately)
Since the present value of $21,600 in 30 years is about $1,238.69 and it is much greater than $200 today, the better choice would be to wait for the $21,600 in 30 years. Therefore, the correct choice is Option 1: Choose $21,600 in 30 years.