Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

interest accrued is: Balance due, times interest:

interest accrued = 1853.42 (.155/12)

payment = principal + interest

ending balance = balance due + interest - payment

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

next month is calculated the same way.

each month is 1/12 of the year.

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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?

Answer 17

the APR doesnt change, that is just the cost of the money that isnt paid back yet.

\[I=B_m(\frac{APR}{12})\]

Answer 18

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

Answer 19

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.

Answer 20

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?

Answer 21

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.

Answer 22

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

Answer 23

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.

Answer 24

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

1/12 * .155 is correct

Answer 25

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

Answer 26

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

Answer 27

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.

Answer 28

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

Answer 29

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

Answer 30

lol, let me do the calculations :)

Answer 31

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

Answer 32

i spose an excel sheet would make life simpler :)

Answer 33

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

Answer 34

Oh, yes it would. Lol.

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

my calcs were wrong, not yours ...

Answer 39

you simplified yours more than I did. Made it easier

Answer 40

I was right than?

Answer 41

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

Answer 42

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

Answer 43

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

Answer 44

Yes, I did. Thank you so much!

Answer 45

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

Answer 46

Nevermind I see it