Help me please !
Barbara opened a store credit card to purchase a game console for $396. She put the entire purchase on the credit card. Her APR is 24.99% and the minimum payment is 5%. Assuming she makes only minimum payments, what is the remaining balance on her card after 3 months?
$362.35
$339.52
$384.45
$351.78

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- anonymous

- katieb

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- amistre64

\[B_n=B_o(1+apr/12)-P\]

- experimentX

hello \( NaOH + HCl - H_20 \)

- amistre64

since the payment is 5% of the Balance
\[P=B_o(1+apr/12)*.05\]
\[B_n=B_o(1+apr/12)-B_o(1+apr/12)*.05\]
\[B_n=B_o(1+apr/12)(1-.05)\]

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## More answers

- amistre64

\[B_1=396(1+\frac{.2499}{12})(.85)\]
\[B_2=B_1(1+\frac{.2499}{12})(.85)\]
\[B_3=B_2(1+\frac{.2499}{12})(.85)\]

- amistre64

ugh ... .95 not .85 :)

- anonymous

how you get (.85) ?

- amistre64

thats easy ... 1 - .05 = .85 when you dont know how to subtract ....
i worked out the recurrsion above in terms of balance and .05 minimum payment

- amistre64

the new balance part of a bill is:
old balance, times (1+apr/12)
we subtract a minimum payment of .05 from it
old balance, times (1+apr/12); minus old balance, times (1+apr/12), times .05
\[B_n=B_{n-1}(1+r)-B_{n-1}(1+r)(.05)\]
\[B_n=B_{n-1}(1+r)[1-.05]\]

- anonymous

idk how you get .85

- anonymous

its 0.95

- amistre64

i know its .95 .... seeing how i am a human being, i tend to miscalculate some simple process. how did i get 1-.05 = .85? its either a typo since 9 and 8 are very close on the keyboard .... or a simply did the subtraction wrong in my head.

- amistre64

the important thing is: a correction is made and we can move on towards a suitable solution

- anonymous

k

- amistre64

\[B_0 = 396\]
\[B_1 = 396(.95)(1+\frac{.2499}{12})\]
\[B_2 = (396(.95)(1+\frac{.2499}{12}))(.95)(1+\frac{.2499}{12})\\~~~~=396(.95)^2(1+\frac{.2499}{12})^2\]
...
\[B_n = 396(.95)^n(1+\frac{.2499}{12})^n\]looks suitable

- amistre64

the question i have is: do we take the balance of the 3rd or the 4th?

- amistre64

start: 396
make a payment, remaining balance is 385
make a payment, remaining balance is 373
make a payment, remaining balance is 362
make a payment, remaining balance is 351

- amistre64

also, is the minimum payment 5% of the original purchase? or is it 5% of the remaining balance?

- amistre64

its usually a % of the remaining balance ...

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