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 ( (1-(1+r)^(-n))/(r) \right )}`

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

So ,
`r = (0.066)/(12) = 0.0055`

Plugging values in the PV formula above we get,

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

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

`\mathbf{84500 = PMT * \left ( (0.231470747)/(0.0055) \right )}`

`\mathbf{84500 = PMT * 42.08559028}`

`\mathbf{(84500)/(42.08559028)= PMT}`

`\mathbf{PMT = 2007.813112}`