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

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,

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

Here,

$\text{PV of annuity=13000},\\\\\text{P=??},\\\\\text{r = 2.8\%\ annually}=\frac{2.8}{12}\text{\%\ monthly}\\\\\text{n=3 years=36 months}$

Putting  the values,

$\Rightarrow 13000=P[\dfrac{1-(1+\frac{2.8}{1200})^{-36}}{\frac{2.8}{1200}}]$

$\Rightarrow 13000=P\times 34.4909$

$\Rightarrow P=\dfrac{13000}{34.4909}$

$\Rightarrow P=376.91$

Therefore, her monthly payment will be $376.91