Answer: The most Todd can afford to pay for the car is $37,002
Explanation:
We would need to calculate the Present Value of the monthly payments assuing the monthly payments are made at the end of each month.
We would use the Present Value Ordinary Annuity Formula,
PV = A [tex][\frac{(1+r)^{N} -1}{r} ][/tex]
Where,
PV = Present value of the annuity
A = Annuity = $415 per month
r = Interest rate compounded annually = 7.3% / 12 = 73/120 %
N = number of periods = 6 years x 12 months/year = 72 Months
PV = A [tex][\frac{(1+r)^{N} -1}{r} ][/tex]
PV = 415 x [tex][\frac{(1+\frac{0.07}{12} )^{72} -1}{\frac{0.07}{12} } ][/tex] = 37001.79
The most Todd can afford to pay for the car is $37,002
