Final answer:
The present value of the car, given the payment terms and interest rate, is $10,853.94, calculated using the present value of annuity formula for four payments of $1,500 each discounted at 7% interest rate.
Step-by-step explanation:
The present value of the car is calculated using the formula for the present value of an annuity. Each payment of $1,500 is made at the beginning of each year for four years, discounted at an annual interest rate of 7%. Therefore, the present value (PV) is calculated as follows:
PV = Pmt × {[(1 - (1 + r)^{-n}) / r]}, where Pmt is the annual payment, r is the interest rate, and n is the number of periods.
PV = $1,500 × {[(1 - (1 + 0.07)^{-4}) / 0.07]} = $1,500 × {[(1 - 0.873439) / 0.07]} = $1,500 × 1.808992 = $2,713.49
Since payments start on January 1, 2023, there is no delay in payments, and we sum up the present values of all four payments. So, total present value is $2,713.49 × 4 = $10,853.94.