According to my instructor with an example she is not teaching this right. Please Help!
A car dealer will sell you a used car for $6,479 with $479 down and payments of $181.18 per month for 36 months. What is the APR? (Use the formula on page 156. Round each answer to the nearest tenth.)

- anonymous

- chestercat

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- RagingSquirrel

me?

- anonymous

not you honey

- anonymous

the set up to get the answer according to the instructor was P= 6,479-479 which would give me 6,000 and then I= 181.18*36 which gives me 6522.48 but i'm pretty unsure of how she got the answer in her example problem because it's not helping here

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## More answers

- RagingSquirrel

Radar to the rescue

- anonymous

I hope so

- radar

The principal is as you say $6,000.00. The payments were $181.18 for 36 months. What was the APR (Annual Percentage Rate) Let me get my algebra book lol will be back

- radar

Meantime Raging Squirrel if you have that info from page 156 please help.

- anonymous

page 156 is confusing

- anonymous

I dont really know how to relate it to the problem that I have

- radar

I see what you mean, my book shows APR when you're saving money not spending it lol. Lets see if we can figure this out. First what was the total payments? That would be 36 X 181.18 are total repaid was $6,522.48 So the amount of interest for three years was $522.48.

- radar

I googled it and it is 5.5 % Now I will try and get that lol

- anonymous

im confused hold on let me write it out again

- anonymous

how did you find out the amount of interest after you multiplied the 181.18 and 36?

- radar

I looked it up on a loan calculator from google lol. Let study this some more, I think I can use the formula for savings, if I can change some things. I found something.

- anonymous

great!

- radar

Here is the formula:
\[288(MN-P) \over N(MN+12P)\]where N=total monthly payments (36)
M=Monthly payment (181.18)
P= Amount financed (6000) Lets try that

- barrycarter

You start out owing 6000. After one month, the amount borrowed
increases by a month's interest on that 6000 (let's call the monthly
interest rate r), but also decreases by your payment 181.18, so your
total owed at the end of month 1 is:
6000*(r+1) - 181.18
For month 2, your loan increases by the interest on the amount above, but
decreases by another 181.18. End of month 2:
(6000*(1+r) - 181.18)*(1+r) - 181.18
For month 3:
((6000*(1+r) - 181.18)*(1+r) - 181.18)*(1+r) - 181.18
For convenience, I'm going to subsitute t for 1+r. Thus, at the end of
month 3, you owe:
-181.18 - 181.18*t - 181.18*t^2 + 6000*t^3
At the end of month 4:
(-181.18 - 181.18*t - 181.18*t^2 + 6000*t^3)*t - 181.18
which simplifies to:
-181.18 - 181.18*t - 181.18*t^2 - 181.18*t^3 + 6000*t^4
or even:
-181.18*(1 + t + t^2 + t^3) + 6000*t^4
The pattern continues, so, after month 36, you owe:
-181.18(1 + t + t^2 + ... + t^35) + 6000*t^36
Simplifying the sum 1 + t + t^2 + ..., we get:
-181.18*(t^36-1)/(t-1) + 6000*t^36
Since we know you owe nothing after 36 months, we set the above equal
to 0, and find that t=1.00458475
This means the monthly interest rate is t-1 or 0.00458475.
The yearly interest rate is thus (1+0.00458475)^12 -1 or 5.64257%
Rounding, that's 5.6%

- anonymous

that's very detailed; however, very difficult to follow Barry

- radar

Thanks barrycarter, using the monthly formula and the values for M,N,P the APR came out as 5.323% This formula came out of my algebra book.

- radar

I have never used that formula before.

- radar

My book did say that the formula was good for finding the "approximate" interest rate.

- radar

Well there you have it twanarain. Good luck with it.

- anonymous

lol thanks guys

- radar

Note that the 5.6 came out close to the 5.5 from the google calculator for loans.

- anonymous

right

- barrycarter

I was trying to show how you could figure this out without having to resort to formulas. Bankrate.com's amortization calculator (http://www.bankrate.com/calculators/mortgages/amortization-calculator.aspx) suggests I'm pretty close:

- anonymous

Thank you Barry I will check it out. I really do appreciate your help.

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