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## NaCl one year ago 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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1. amistre64

$B_n=B_o(1+apr/12)-P$

2. experimentX

hello $$NaOH + HCl - H_20$$

3. amistre64

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

4. amistre64

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

5. amistre64

ugh ... .95 not .85 :)

6. NaCl

how you get (.85) ?

7. 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

8. 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 $B_n=B_{n-1}(1+r)-B_{n-1}(1+r)(.05)$ $B_n=B_{n-1}(1+r)[1-.05]$

9. NaCl

idk how you get .85

10. NaCl

its 0.95

11. 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.

12. amistre64

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

13. NaCl

k

14. 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

15. amistre64

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

16. 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

17. amistre64

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

18. amistre64

its usually a % of the remaining balance ...

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