Final answer:
The amount of the car bought, financed for 60 months at 12% annual interest compounded monthly with a $550 monthly payment and no down payment, is approximately $24,725.58.
Step-by-step explanation:
To determine the amount of car bought if it was financed for 60 months with no down payment, at 12% annual interest, compounded monthly with a $550 monthly car payment, we can use the formula for the present value of an annuity:
PV = R * [(1 - (1 + i)^-n) / i]
Where:
- PV is the present value or the amount of the car loan
- R is the monthly payment amount
- i is the monthly interest rate (annual rate / 12)
- n is the total number of payments
By plugging in the values:
PV = $550 * [(1 - (1 + 0.01)^-60) / 0.01]
PV = $550 * 44.9556
PV = $24,725.58
So, the amount of the car bought is approximately $24,725.58. This demonstrates the cost of the vehicle a customer can afford without making a down payment and taking into account the loan terms and interest rate.