Q:

trevon had a credit score of 750. he will be bying a new oickuo that costs $38,000 with a down payment of $8,000. calculate his monthly payment plan for a 5 yr payment plan

Accepted Solution

A:
To solve this problem, we are going to the loan payment formula: [tex]P= \frac{( \frac{r}{n})PV }{1-(1+ \frac{r}{n})^{-nt} } [/tex]
where
[tex]P[/tex] is the regular payment.
[tex]PV[/tex] is the present value. 
[tex]r[/tex] is the interest rate in decimal form. 
[tex]n[/tex] number of times the regular payment is made per year.
[tex]t[/tex] is number of years.

As  of May 2018, the new car loan rate for a credit score of 750 is 3.59%. Now, to convert the rate to decimal form, we are going to divide it by 100%:
[tex]r= \frac{3.59}{100}[/tex]
[tex]r=0.0359[/tex].
Since the down payment is $8,000, we are going to subtract that form $38,000 to get our present value:
[tex]PV=38000-8000[/tex]
[tex]PV=8000[/tex]
We know that the payments are going to be monthly, so [tex]n=12[/tex]. 
Since we are making a payment plan for 5 years, [tex]t=5[/tex]. 

Lets replace the values in our formula:

[tex]P= \frac{( \frac{r}{n})PV }{1-(1+ \frac{r}{n})^{-nt} } [/tex]
[tex]P= \frac{( \frac{0.0359}{12})30000 }{1-(1+ \frac{0.0359}{12})^{-(12)(5)} } [/tex]
[tex]P= \frac{30000( \frac{0.0359}{12}) }{1-(1+ \frac{0.0359}{12})^{-60} }[/tex]
[tex]P=546.96[/tex]

We can conclude that Trevor's monthly payment will be $546.96