Final answer:
To decide whether Rafael would prefer $1,000 today or $1,500 in five years, we calculate the present value of the $1,500 assuming an 8% return rate. Using the formula PV = FV / (1 + r)^n, we can find the present value to compare it with $1,000. Rafael's choice depends on whether this present value is more or less than $1,000.
Step-by-step explanation:
To determine whether Rafael would prefer $1,000 today or $1,500 in five years, we use the concept of present value and compound interest. Given an 8 percent after-tax rate of return, we need to calculate the present value of $1,500 received in five years. The present value (PV) formula is PV = FV / (1 + r)^n, where FV is the future value, r is the rate of return per period, and n is the number of periods. In Rafael's case, FV is $1,500, r is 0.08 (or 8%), and n is 5 years.
Thus, the calculation becomes PV = $1,500 / (1 + 0.08)^5. When we calculate this, the result gives us the equivalent value of $1,500 in today's dollars, assuming an 8% rate of return over the five years. If the present value is greater than $1,000, Rafael would prefer the $1,500 in five years; if it is less, he would prefer $1,000 today.
Rafael would prefer to receive $1,000 today rather than $1,500 in five years. This is because of the concept of time value of money and the opportunity to earn a rate of return on the money. By investing $1,000 today and earning an 8 percent rate of return, Rafael's investment will grow over time. Let's calculate the future value of $1,000 after five years:
Future Value = Present Value * (1 + Interest Rate)^Time
The future value of $1,000 after five years at an 8 percent rate of return would be $1,469.33. Comparing this to $1,500 in five years, it is clear that Rafael would be better off taking $1,000 today.
In summary, Rafael would prefer $1,000 today over $1,500 in five years because he can invest the money and earn a rate of return, which would result in a higher future value than $1,500.