Question

you want to buy a new car, but you can make an initial payment of only $2,400 and can afford monthly payments of at most $500.

Answer 1

Maximum price we can pay for the car if the purchase is financed over 48 months = $21,386.98

If the APR on auto loans is 12% and you finance the purchase over 48 months, what is the maximum price you can pay for the car?

Generally, the equation for PV is  mathematically given as

$\mathrm{PV}=\quad \mathrm{C} * \frac{1-\left[1 /(1+r)^{\wedge} \mathrm{n}\right]}{\mathrm{r}}$

C= Monthly Amount = 500

r= Interest Rate Per Period =12 %=0.12 / 12=0.001

n= Number of Periods =48 Months =48 Periods

Therefore

$= 500^* \frac{1-\left[1 /(1+0.01)^{\wedge} 48\right]}{0.01}$

$\begin{aligned}&=\ 500^* \frac{1-\left[1 /(1.01)^{\wedge} 48\right]}{0.01} \\\\&=\ 500^* \frac{1-[1 / 1.612226078]}{0.01} \\\\&=\ 500 * \frac{1-0.620260405}{0.01}\end{aligned}$

In conclusion,

$= 500^* \frac{0.379739595}{0.01}\\\\=\ 500^*37.9739595\\\\=\ 18,986.98$

Maximum price we can afford:

= Initial Payment + Present value of monthly payments

=$ 2,400+$ 18,986.98

=$ 21,386.98

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CQ

you want to buy a new car, but you can make an initial payment of only $2,400 and can afford monthly payments of at most $500.

If the APR on auto loans is 12% and you finance the purchase over 48 months, what is the maximum price you can pay for the car? (Do not round intermediate calculations. Round your answer to 2 decimal places.)