Question 1200898
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Part (a)


The car is priced at $12,000
The buyer puts 25% down, so the remaining 75% is loaned.


75% of 12000 = 0.75*12000 = 9000 dollars is the loan amount


We'll be using this monthly payment formula
P = (L*i)/( 1 - (1+i)^(-n) )
where,
P = monthly payment
L = loan amount
i = decimal form of the monthly interest rate
n = number of months


In this case,
P = unknown
L = 9000
i = 0.06/12 = 0.005
n = 48 for now (we'll use n = 60 later)


So,
P = (L*i)/( 1 - (1+i)^(-n) )
P = (9000*0.005)/(1 - (1+0.005)^(-48))
P = 211.365261431424
P = 211.37
This is the monthly payment if you go for the 48 month (aka 4 year) plan.


This calculator may come in handy
<a href = "https://www.calculator.net/loan-calculator.html">https://www.calculator.net/loan-calculator.html</a>


We'll repeat very similar steps for the 5 year plan, but use n = 60 this time. Keep everything else the same.
P = (L*i)/( 1 - (1+i)^(-n) )
P = (9000*0.005)/(1 - (1+0.005)^(-60))
P = 173.995213764854
P = 174.00
This is the monthly payment if you go for the 60-month plan.



Summary:
Monthly payment for 48 months: <font color=red>$211.37</font>
Monthly payment for 60 months: <font color=red>$174</font>


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Part (b)


Over the course of 48 months, the monthly payment is $211.37 calculated earlier in part (a).


Therefore, you'll pay back a total of 48*211.37 = 10,145.76 dollars.
Subtract off the loan amount ($9000) to compute the interest
10,145.76 - 9,000 = 1,145.76


Follow the same outline for the 60-month plan.
(60 months)*($174 per month) = 10440 dollars paid back 
10440 - 9000 = 1440
You pay slightly more interest due to the longer lifespan of the loan. 


Summary:
Interest charged for 48 months: <font color=red>$1,145.76</font>
Interest charged for 60 months: <font color=red>$1440</font>
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