SOLUTION: The price of a new car is $12,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 6%/year

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The price of a new car is $12,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 6%/year      Log On


   

Question 1200898: The price of a new car is $12,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 6%/year compounded monthly. (Round your answers to the nearest cent.)
(a) What monthly payment will she be required to make if the car is financed over a period of 48 months? Over a period of 60 months?
48 months:
60 months:
(b) What will the interest charges be if she elects the 48-month plan? The 60-month plan?
48-month plan:
60-month plan:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

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
https://www.calculator.net/loan-calculator.html

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: $211.37
Monthly payment for 60 months: $174

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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: $1,145.76
Interest charged for 60 months: $1440