I need some help with some consumer math, please. ^.^

- SnowWhite007

I need some help with some consumer math, please. ^.^

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- SnowWhite007

You owe $1,853.42 on a credit card with a limit of $3,000.00 at a rate of 15.5% APR. You pay $400.00 the first 2 months and then $200.00 until the bill is paid off. You pay the bill on the due date each month. (The thing below is suppose to be a a table. ^.^)
Month 1 2 3 4 5 6 7 8 9 10
Principal
Interest accrued
Payment (on due date)
End-of-month balance

- amistre64

so what are your thoughts on how to fill it out?

- SnowWhite007

okay, I think the equation has to do with. taking the original number and taking the APR and then subtracting the 400, correct?

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## More answers

- amistre64

that appears to be a good approach, what is your equation?

- amistre64

and i think APR is given as a year value, and we need to adjust it for a month value

- SnowWhite007

I plug in the numbers but the amount comes out to be more then the original amount.

- SnowWhite007

It's after the first month, so 1453.42(1.15) - 400

- amistre64

interest accrued is: Balance due, times interest:
interest accrued = 1853.42 (.155/12)
payment = principal + interest
ending balance = balance due + interest - payment

- SnowWhite007

okay, so where did the 12 come from in the interest accrued area, may I ask?

- amistre64

the interest given (APR) is a year value. the time between payments is 1/12 of a year (a month)
so the interest applied is not a full years interest

- SnowWhite007

Oh! I get it. So then the next month it would turn into 2/12, right?

- amistre64

next month is calculated the same way.
each month is 1/12 of the year.

- SnowWhite007

Why's that? I'm confused again. Sorry.

- amistre64

as the value of the loan changes, the value of the accrued interest is based off the new/remaining balance (what you owe change)

- SnowWhite007

So, the APR would not change, just the original and final amount?

- amistre64

spose you owe me $20, and give me 5
our situation changes from 20 to 15 ... i do not keep asking for 20 do i?

- amistre64

the APR doesnt change, that is just the cost of the money that isnt paid back yet.
\[I=B_m(\frac{APR}{12})\]

- SnowWhite007

No. You'd ask for 15. But, how does that apply to the APR and the amount given and taken.?

- amistre64

the APR is the cost of the loan.
at first the loan is 20. the cost on 20 is the interest you pay ....
the loan is altered to 15, we basically have to restructure the loan now and base it off of a loan of 15 instead
say another 3 dollars is paid back .... we would restructure the loan with a balance of 12 now ...
each payment made alters the size of the loan ... the cost to borrow money is still going to be (15.5%) but it is the amount of money that is being loaned that changes.

- SnowWhite007

So, the amount owed changes but the APR percentage stays the same. You continue to pay it off but the 15.5% do not change. Right? Am I getting it?

- amistre64

that is correct.
the amount of money 'loaned out' changes from month to month, but the cost of borrowing money (15.5%) is the same regardless of how much money is being loaned.

- SnowWhite007

So the equation is 1,853.42* (1/12 * 1.55) - 400 for the first month or am I wrong?

- amistre64

the repetition of events is:
we start with a balance owed: B
we accrue a months worth of interest: B(i/12)
we make a payment: P
we calculate the ending result: B + B(i/12) - P
-----------------------
the payment can be broken down into 2 parts: interest accrued, and principal.

- amistre64

1/12 * 1.55 is not good ... maybe a mistype.
1/12 * .155 is correct

- SnowWhite007

Oh. I think I understand. Would you like to do the first two months with me to make sure I understand, please?

- amistre64

sure, let me see your attempt at the first month and see if i need to correct it :)

- SnowWhite007

okay. So, B + B(i/12) - P
1,853.42 + 1,853.42(.155/12) - 400
1,853.42 + 23.94 - 400
1,477.36 in the final amount for the first month.

- amistre64

very good. i get the same results
APR = 15.5%
Beginning balance:1853.42
Payment: 400
Interest Accrued: 1853.42(.155/12) = 23.94
Principal: 400-23.94 = 376.06
Ending balance: 1853.42-376.06 = 1477.36

- SnowWhite007

Yay!
So the second month would be 1,096.44?

- amistre64

lol, let me do the calculations :)

- amistre64

We agree :) you are doing very well
Ending/Starting balance: 1477.36
-----------------------------------------
Payment: 400
Interest Accrued: 1477.36(.155/12) = 19.08
Principal: 400-23.94 = 380.92
Ending balance: 1477.36-380.92 = 1096.44

- amistre64

i spose an excel sheet would make life simpler :)

- SnowWhite007

So the 3rd month goes to paying 200 it'd be 910.60 right?

- SnowWhite007

Oh, yes it would. Lol.

- amistre64

Ending balance: 1477.36-380.92 = 1096.44
-----------------------------
Payment: 200
Interest Accrued: 1096.44(.155/12) = 14.16
Principal: 200-14.16 = 185.84
Ending balance: 1096.44-185.84 = 896.44

- SnowWhite007

Where'd I go wrong on this one? I see the information, but Still slightly confused. I understand the first months, but now what. lol

- SnowWhite007

I see it now. I worked it out a little more.

- amistre64

my calcs were wrong, not yours ...

##### 1 Attachment

- SnowWhite007

you simplified yours more than I did. Made it easier

- SnowWhite007

I was right than?

- amistre64

you was right, i hit the wrong button on the calculator ... :)

- SnowWhite007

Lol. Thank you so much for your help. I sorry I kept you so long, but I appreciate the help so much. :) I wish I could give you like, 10 metals at once, but OpenStudy doesn't have that feature. :D

- amistre64

:) as long as you learned how to process this its all good

- SnowWhite007

Yes, I did. Thank you so much!

- anonymous

Excuse me I'm doing this right now and for the principal does it stay the same?? I'm confused about that.

- anonymous

Nevermind I see it

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