Respuesta :
Answer:
The monthly payment is $241.76.
Step-by-step explanation:
Given : Suppose you take out a car loan for $9999 for 4 years at a 7.5% interest rate.
To find : What is your monthly payment ?
Solution :
The formula to find monthly payment is
[tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
Discount factor is [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
Substitute in the formula,
[tex]M=\frac{A}{\frac{1-(1+i)^{-n}}{i}}[/tex]
[tex]M=\frac{A\times i}{1-(1+i)^{-n}}[/tex]
where, A is the amount A=$9999
r is the rate =7.5%=0.075
[tex]i=\frac{r}{12}=\frac{0.075}{12}=0.00625[/tex]
time t=4 years
Time in months [tex]n=t\times 12=4\times 12=48[/tex]
Substitute all the values in the formula,
[tex]M=\frac{9999\times 0.00625}{1-(1+0.00625)^{-48}}[/tex]
[tex]M=\frac{62.49375}{1-(1.00625)^{-48}}[/tex]
[tex]M=\frac{62.49375}{1-0.7415101}[/tex]
[tex]M=\frac{62.49375}{0.25848}[/tex]
[tex]M=241.76[/tex]
Therefore, the monthly payment is $241.76.
