Answer: The monthly payment will be $2007.81.
We have:
Cost of the sports coupe (PV) $84,500
Annual Percentage Rate (APR) 6.6%
Loan tenure in months (n) 48
We can find the monthly payment by using the Present value of an annuity formula:
[tex]\mathbf{PV_{Annuity}= PMT * \left ( \frac{1-(1+r)^{-n}}{r} \right )}[/tex]
Since APR is a yearly number, we need to convert it into a monthly rate.
So , [tex]r = \frac{0.066}{12} = 0.0055[/tex]
Plugging values in the PV formula above we get,
[tex]\mathbf{84500 = PMT * \left ( \frac{1-(1+0.0055)^{-48}}{0.0055} \right )}[/tex]
[tex]\mathbf{84500 = PMT * \left ( \frac{1-0.768529253}{0.0055} \right )}[/tex]
[tex]\mathbf{84500 = PMT * \left ( \frac{0.231470747}{0.0055} \right )}[/tex]
[tex]\mathbf{84500 = PMT * 42.08559028}[/tex]
[tex]\mathbf{\frac{84500}{42.08559028}= PMT}[/tex]
[tex]\mathbf{PMT = 2007.813112}[/tex]
