Final answer:
To determine the maximum price you can pay for the car with an initial payment of $2,000 and monthly payments of at most $400 over 48 months, you need to use the present value of an annuity formula. The maximum price is $13,251.44. For a 60-month financing, the maximum price is $15,293.40.
Step-by-step explanation:
To determine the maximum price you can pay for the car with an initial payment of $2,000 and monthly payments of at most $400 over 48 months, you need to use the formula for the present value of an annuity. The formula is:
PV = C * (1 - (1 + r)^(-n)) / r
Where PV is the present value, C is the monthly payment, r is the monthly interest rate (APR/12), and n is the number of months.
For this case, the monthly payment C = $400,
the interest rate r = 12%/12
= 0.01, and
the number of months n = 48.
Plugging in the values, we get:
PV = 400 * (1 - (1 + 0.01)^(-48)) / 0.01
= $13,251.44
Therefore, the maximum price you can pay for the car is $13,251.44.
If you finance the purchase over 60 months, the number of months n will be 60. Plugging in the values into the formula, we get:
PV = 400 * (1 - (1 + 0.01)^(-60)) / 0.01
= $15,293.40
Therefore, if you finance the purchase over 60 months, the maximum price you can pay for the car is $15,293.40.