Final answer:
Preferring $48 now over $50 in a month implies a monthly interest rate of about 4.17%, which translates to an annual interest rate of approximately 63%. Hence, option (a) 63% is the correct choice.
Step-by-step explanation:
When considering whether preferring $48 now instead of $50 in a month implies an annual interest rate, we are dealing with the concepts of time value of money and discount rates. If one would rather have a smaller amount of money now than wait for a slightly larger amount later, then the immediate cash is being regarded as more valuable. This implies there is a certain interest rate at which you'd be indifferent to having the money now or later.
The calculation to find this annual interest rate is as follows: FV / (1 + r) = PV, where FV is the future value, r is the interest rate, and PV is the present value. Rearranging this formula to solve for the interest rate gives us r = (FV / PV) - 1. Substituting the given values from the question, we have r = ($50 / $48) - 1, which is approximately 0.0417 or 4.17% for one month.
To convert this monthly rate to an annual interest rate, we use the formula (1 + monthly rate)^12 - 1. Plugging in our monthly rate, we get (1 + 0.0417)^12 - 1, which is approximately 0.63 or 63% on an annual basis. Therefore, the correct answer to the question is option (a) 63%.