Question

Bob Rohrman is offering a 2016 Toyota Camry for $29,000. If you have a $5,000 down payment and are able toborrow the rest at a 2.99% APR on a 48 month loan, how much will your payments be? (round to the hundredthsplaces)

Answer 1

Answer:

The monthly payments are $513.12

Step-by-step explanation:

The formula to calculate the monthly payment is:

$P=\frac{r\left(PV\right)}{1-\left(1+r\right)^{-n}}$

Where:

• P, is the monthly payment

,

• PV, is the present value

,

• r, is the rate per period

,

• n, is the number of periods

After a $5,000 down payment, the present value (PV) would be:

$\begin{gathered} 29000-5000=24000 \\ \rightarrow PV=24000 \end{gathered}$

Now, let's transform the APR into the rate per period:

$\begin{gathered} 2.99\%\rightarrow0.0299\rightarrow\frac{0.0299}{12} \\ \\ \rightarrow r=\frac{0.0299}{12} \end{gathered}$

Since the loan is for 48 months, we'll have 48 periods. This way,

$n=48$

Using all this data in the original formula, we'll get the following:

$\begin{gathered} P=\frac{r(PV)}{1-(1+r)^{-n}}\rightarrow P=\frac{\frac{0.0299}{12}(24000)}{1-(1+\frac{0.0299}{12})^{-48}} \\ \\ \Rightarrow P=513.12 \end{gathered}$

Therefore, we can conlude that the monthly payments are $513.12