Answer-
- Monthly payment = $363.66
- Total interest = $3184.6
Solution-
Formula used-
[tex]\text{PV of annuity}=P[\dfrac{1-(1+r)^{-n}}{r}][/tex]
Cost of the car = $26635
Down-payment amount = $8000
So, Present Value of the annuity = 26635-8000 = $18635
r = rate of interest = 6.39% annual = [tex]\dfrac{6.39}{12}[/tex]% monthly
n = time period = 5 years = 60 months
Putting the values in the formula,
[tex]\Rightarrow 18635=P[\dfrac{1-(1+\dfrac{0.0639}{12})^{-60}}{\dfrac{0.0639}{12}}][/tex]
[tex]\Rightarrow P=\dfrac{18635}{[\dfrac{1-(1.005325)^{-60}}{0.005325}]}[/tex]
[tex]\Rightarrow P=\dfrac{18635\times 0.005325}{1-(1.005325)^{-60}}[/tex]
[tex]\Rightarrow P=\$363.66[/tex]
Hence, your monthly payment will be $363.66
The total amount you will be paying in 5 years (including down-payment) is, [tex]8000+(363.66\times 60)=8000+21819=\$29819.6[/tex]
Therefore, the total interest for the loan will be [tex]29819.6-26635=\$3184.6[/tex]
