Final answer:
The student is asked to compare two financial offers for a used car by calculating the present value of each offer using a given interest rate. They need to determine which offer has a higher present value to decide which is more beneficial for the car dealership.
Step-by-step explanation:
The question is about comparing two financial offers for a used car to determine which one is more beneficial for a car dealership, given a nominal quarterly interest rate of 7%. To solve this, the dealership needs to calculate the present value of both offers using the given interest rate and compare them to decide which offer has a higher current worth and should be accepted.
First, we calculate the present value of the first offer of $5,000 today and $5,000 in 6 months. For the second offer, we calculate the present value of $5,500 today and $4,500 in 12 months. Since the interest is quoted as a nominal quarterly rate, it means that interest is compounded four times a year. We would use this rate to discount future payments to their present values.
The present value (PV) of a future payment can be calculated using the formula:
PV = FV / (1 + r)n
Where FV is the future payment, r is the periodic interest rate, and n is the number of periods before the payment is received.