Question

How would I set this up?

Karen uses her credit card to purchase a new television for $695.20. She can pay off up to $325 per month. The card has an annual rate of 17.9% compounded monthly. How much will she pay in interest?

Answer 1

Bnew = Bold k - P

when Bnew = 0, its paid off, add up all the payments made and subtract off the original amount to see how much you paid for the convience of being broke ...

Answer 2

I would set it up as:
\[0=Bk^n-P\frac{1-k^n}{1-k}\]
\[Bk^n=P\frac{1-k^n}{1-k}\]
\[\frac BPk^n(1-k)=1-k^n\]
\[\frac BP(1-k)=k^{-n}-1\]
\[\frac BP(1-k)+1=k^{-n}\]
\[log\left(\frac BP(1-k)+1\right)=-n~logk\]
\[\frac{log\left(\frac BP(1-k)+1\right)}{-logk}=n\]
to evaluate the number of payments

Answer 3

in this case, k = 1+.179/12

Answer 4

What does be stand for?

Answer 5

the original balance to payoff

Answer 6

it will take 2 months and a little more to pay off

Answer 7

http://www.wolframalpha.com/input/?i=-log%28695.20%281-%281%2B.179%2F12%29%29%2F325%2B1%29%2Flog%281%2B.179%2F12%29

Answer 8

I'm not look for the months though. I need to find out how much she will pay in interest

Answer 9

@manguitar I don't see how that is helpful in anyway...

Answer 10

you need to know how many payments are made, and since the payments are made each month ... you need to know how many months it takes to payoff

Answer 11

it is trust me 2 dollars full of chicken!

Answer 12

Oh! Okay, that makes sense @amistre64

Answer 13

we can work this longhand since its so short:

695.20 = starting balance

first payment: 695.20(1+.179/12) - 325 = 380.57

second payment: 380.57(1+.179/12) - 325 = 61.25

second payment: 61.25(1+.179/12) = 62.16

so a total payment amount of 325 + 325 + 62.16 gives us the amount of the original balance plus interest

Answer 14

lol, the last payment is a third

Answer 15

and full of chicken

Answer 16

712.16 is what i determine for total payments; subtract off the 695.20 to determine the excess paid in interest.

the amount for "n" (2.19) that i originally determined would have given us a total payment of: 325(2.19) = 711.75 since it assumes that it doesnt take a full 3 months and ignores the remaining days of the third month. but its pretty close :)

Answer 17

...and full of chickens i spose

Answer 18

yes full of chickens

Answer 19

Sorry for the delayed reply, I'm a little confused on that last paragraph you sent

Answer 20

@amistre64

Answer 21

i was just comparing the longhanded version with the first approach i used.

Answer 22

if we work out the accumulation of interest and the payments made, we get a total payout of:
325 + 325 + 62.16 = 712.16

this total payment amount covers the original balance, plus interest

712.16 = 695.20 + int paid

712.16 - 695.20 = int paid

Answer 23

So, the final answer would be $16.96?

Answer 24

with any luck, yes :)

Answer 25

$16.96 full of chicken @AdrianK

Answer 26

Thank you so much! You were really helpful! @amistre64 :D

Answer 27

youre welcome

Answer 28

don't forget full of chicken