Answer:
Monthly payment is $839.83
Step-by-step explanation:
Given : Teresa is buying a car for $23,550. She will finance $19,600 of it with a 2-year loan at 2.7% APR.
To find : What will her monthly auto payment be?
Solution :
Formula of monthly payment,
Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
Discount factor [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
Where, Amount = $19,600
Rate r= 2.7%=0.027
[tex]i=\frac{0.027}{12}=0.00225[/tex]
Time = 2 years
[tex]n=2\times12=24[/tex]
Now, put all the values we get,
[tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
[tex]D=\frac{1-(1+0.00225)^{-24}}{0.00225}[/tex]
[tex]D=\frac{1-(1.00225)^{-24}}{0.00225}[/tex]
[tex]D=\frac{1-0.94748}{0.00225}[/tex]
[tex]D=\frac{0.0525}{0.00225}[/tex]
[tex]D=23.337[/tex]
Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
[tex]M=\frac{19600}{23.337}[/tex]
[tex]M=839.83[/tex]
Therefore, Monthly payment is $839.83
