Question

Maria is buying a car for $18,510. She will finance $13,000 of it with a 3-year loan at 2.8% APR. What will her monthly auto payment be?

Answer 1

Answer-

Maria's monthly payment will be $376.91

Answer 2

Maria's monthly payment will be $376.91

Solution-

Maria is buying a car worth of $18,510, but she will finance only $13,000 of it with a 3-year loan at 2.8% APR.

We know that,

`\text{PV of annuity}=P[(1-(1+r)^(-n))/(r)]`

Here,

`\text{PV of annuity=13000},\\\\\text{P=??},\\\\\text{r = 2.8\%\ annually}=(2.8)/(12)\text{\%\ monthly}\\\\\text{n=3 years=36 months}`

Putting the values,

`\Rightarrow 13000=P[(1-(1+(2.8)/(1200))^(-36))/((2.8)/(1200))]`

`\Rightarrow 13000=P* 34.4909`

`\Rightarrow P=(13000)/(34.4909)`

`\Rightarrow P=376.91`

Therefore, her monthly payment will be $376.91