Maximum price we can pay for the car if the purchase is financed over 48 months = $21,386.98
Generally, the equation for PV is mathematically given as
[tex]$\mathrm{PV}=\quad \mathrm{C} * \frac{1-\left[1 /(1+r)^{\wedge} \mathrm{n}\right]}{\mathrm{r}}$[/tex]
C= Monthly Amount = 500
r= Interest Rate Per Period =12 %=0.12 / 12=0.001
n= Number of Periods =48 Months =48 Periods
Therefore
[tex]= 500^* \frac{1-\left[1 /(1+0.01)^{\wedge} 48\right]}{0.01}[/tex]
[tex]\begin{aligned}&=\$ 500^* \frac{1-\left[1 /(1.01)^{\wedge} 48\right]}{0.01} \\\\&=\$ 500^* \frac{1-[1 / 1.612226078]}{0.01} \\\\&=\$ 500 * \frac{1-0.620260405}{0.01}\end{aligned}[/tex]
In conclusion,
[tex]= 500^* \frac{0.379739595}{0.01}\\\\=\$ 500^*37.9739595\\\\=\$ 18,986.98$[/tex]
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.)
