Question

Jim made a down payment of 1000 dollars toward the purchase of a car. To pay the balance of the purchase price, he has secured a loan from his bank at the nominal rate of 7.2 percent per year compounded monthly. Under the terms of his finance agreement, he is required to to make payments of 210 dollars per month for 36 months.
What is the cash price of the car?
How much, in total, will Jim spend on interest charges?

Answer 1

I assume the amount he pays each month includes the interest
Total amount he pays to the bank = 210x36 = $7560
Let n be the amount he borrowed.
n x [1+ (7.2% / 12)] ^ 36 = 7560
n x 1.006^36 = 7560
n = calculate it yourself..
cash price of the car = down payment + n = 1000 +n =do it yourself

interest charge = 7560 -n = do it yourself :P

Answer 2

Got the wrong answer :(

Answer 3

According to your equations, n = 6095.29, price = 7095.29, and interest charge = 1464.71
But that's incorrect. Any other ways to solve please?

Answer 4

Does the payment include the interest?

Answer 5

I'm not sure but that's all the info they've given us

Answer 6

The other 'way' I could think of it that the payment does not include the interest
amount he borrowed = amount he pays = 210x36 = 7560
cash price = amount borrowed + down payment = work it out
Interest = amount he borrowed x [1+ (7.2% / 12)] ^ 36 = 7560 x 1.006^36 = calculate it
Try and see if you can get the answer..

Answer 7

Sorry Interest = amount he borrowed x [1+ (7.2% / 12)] ^ 36 - 7560= 7560 x 1.006^36 -7560 = calculate it

Answer 8

Both answers are still incorrect..

Answer 9

If the cost of the car is ($ 6781.06 + initial down payment of 1000) = 7781.06, then I will post my work.

Answer 10

Yeah that's right!

Answer 11

Well, I'll post my work but first have to say that the formula used is one I've not seen before in math class but found on a website for car dealers.

That said, hold on, and I'll post the work.

Answer 12

x is the amount financed and does not include the $1000 down payment.

210 = x(.072/12)/(1 - (1+.072/12)^-36)

Over at the Wolfram calculator, x was found to be $ 6781.06. Add the $1000.00 to get $ 7781.06 --> total cost of car. (We still have the interest to figure.)

You can see the "wolf work" at this link: http://www.wolframalpha.com/input/?i=210+%3D+x%28.072%2F12%29%2F%281+-+%281%2B.072%2F12%29%5E-36%29

http://teachertech.rice.edu/Participants/bchristo/lessons/carpaymt.html

Answer 13

Now, we'll try to get the interest on $6,781.06 at 7.2% for 36 months with payments of $210 per month. I'll check for one of the auto dealer formulas.

Answer 14

Thanks a lot :) :)

Answer 15

So far, I have not been able to find the total interest. It's not a simple interest type thing but some type of amortization.

There has to be a formula because these online calculators use those algorithms to make the calculators work.

The total amount of interest paid is $778.94.
I'll continue to look for a crank it out formula.

http://www.statefarm.com/learning/calc/carloan.asp

Answer 16

Is $778.94 the correct total interest?

Answer 17

Probably $778.94 is the interest

Answer 18

Yes it's correct. Thanks again