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, \(M=\frac{\text{Amount}}{\text{Discount factor}}\)
Discount factor \(D=\frac{1-(1+i)^{-n}}{i}\)
Where, Amount = $19,600
Rate r= 2.7%=0.027
\(i=\frac{0.027}{12}=0.00225\)
Time = 2 years
\(n=2\times12=24\)
Now, put all the values we get,
\(D=\frac{1-(1+i)^{-n}}{i}\)
\(D=\frac{1-(1+0.00225)^{-24}}{0.00225}\)
\(D=\frac{1-(1.00225)^{-24}}{0.00225}\)
\(D=\frac{1-0.94748}{0.00225}\)
\(D=\frac{0.0525}{0.00225}\)
\(D=23.337\)
Monthly payment, \(M=\frac{\text{Amount}}{\text{Discount factor}}\)
\(M=\frac{19600}{23.337}\)
\(M=839.83\)
Therefore, Monthly payment is $839.83
