Question

Todd can afford to pay $380 per month for the next 5 years in order to purchase a new car. The interest rate is 6.6 percent compounded monthly. What is the most he can afford to pay for a new car today?

• $19,101.44

• $18,406.14

• $20,020.71

• $19,374.88

• $26,925.49

Answer 1

Monthly payment = $380
Number of payments = 60 (5 years)
Annual interest rate = 6.60%
Monthly interest rate = 0.55%

Present value of monthly payments = $380/1.0055 + $380/1.0055^2 + .... + $380/1.0055^59 + $380/1.0055^60
Present value of monthly payments = $380 * (1 - (1/1.0055)^60) / 0.0055
Present value of monthly payments = $380 * 50.986533
Present value of monthly payments = $19,374.88

So, Todd can afford to pay a maximum sum of $19,374.88 of a new car today