Question

You want to buy a new sports coupe for $84,500, and the finance office at the dealership has quoted you an apr of 6.6 percent for a 48 month loan to buy the car. what will your monthly payments be?

Answer 1

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:

$\mathbf{PV_{Annuity}= PMT * \left ( \frac{1-(1+r)^{-n}}{r} \right )}$

Since APR is a yearly number, we need to convert it into a monthly rate.

So , $r = \frac{0.066}{12} = 0.0055$

Plugging values in the PV formula above we get,

$\mathbf{84500 = PMT * \left ( \frac{1-(1+0.0055)^{-48}}{0.0055} \right )}$

$\mathbf{84500 = PMT * \left ( \frac{1-0.768529253}{0.0055} \right )}$

$\mathbf{84500 = PMT * \left ( \frac{0.231470747}{0.0055} \right )}$

$\mathbf{84500 = PMT * 42.08559028}$

$\mathbf{\frac{84500}{42.08559028}= PMT}$

$\mathbf{PMT = 2007.813112}$