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anonymous

  • 5 years ago

A customer purchased items costing $360 with a national credit card that charges 1.5% interest per month compounded monthly. a. Write a recurrence relation and initial conditions for bn, the balance after n months if no further charges occur and the minimum monthly payment of $25 is made. b. Find a general solution of the recurrence relation and the solution for this discrete dynamical system. c. Give the value of the account after 12 months, i.e., b(12).

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  1. anonymous
    • 5 years ago
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    I have some it...just need some extra guidance

  2. anonymous
    • 5 years ago
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    \[b_{0} = 360 \]

  3. anonymous
    • 5 years ago
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    \[b_{n}=1.015b_{n-1} - 25 for n >0\]

  4. anonymous
    • 5 years ago
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    I have c at $104.40

  5. amistre64
    • 5 years ago
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    B{0} = -360 right? since its debt?

  6. anonymous
    • 5 years ago
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    I would think it is just 360 applying debt as initial amount

  7. amistre64
    • 5 years ago
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    we can either look at it as the balance approaching zero from the left; or from the right i spose

  8. anonymous
    • 5 years ago
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    used positive for amortized problem and got that part right

  9. amistre64
    • 5 years ago
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    B{n+1} = B{n}(1.015) - 25 looks right for a recurence equation

  10. anonymous
    • 5 years ago
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    I have a chart so take from balance standpoint

  11. amistre64
    • 5 years ago
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    B0 = 360 B1 = 360(1.015) -25 B2 = (360(1.01) -25)(1.015)-25 B3 = (360(1.01) -25)(1.01)-25)(1.015)-25 right?

  12. anonymous
    • 5 years ago
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    yes

  13. anonymous
    • 5 years ago
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    360(1.015)

  14. amistre64
    • 5 years ago
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    i really got no idea how to go from there ;)

  15. anonymous
    • 5 years ago
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    ok

  16. amistre64
    • 5 years ago
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    the general solution is the homogenous?

  17. anonymous
    • 5 years ago
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    yes

  18. amistre64
    • 5 years ago
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    b0 = 360 b1 = 316.98 b2 = 295.16 b3 = 273.11 b4 = 250.84 b5 = 228.35 b6 = 205.64 b7 = 182.69 b8 = 159.52 b9 = 136.11 b10 = 112.47 b11 = 88.60 b12 = 64.49 these about right?

  19. anonymous
    • 5 years ago
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    I have 360, 340.4, 320.5, 300.3, 279.80, 259, 237.9...

  20. amistre64
    • 5 years ago
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    i always round up when working in money

  21. amistre64
    • 5 years ago
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    ack!!.. i did all that with 1.01 lol

  22. amistre64
    • 5 years ago
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    there is a techniques refered to as variation of parameters that looks very close to this procedure... but i havent grasped it yet.

  23. amistre64
    • 5 years ago
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    in general; you are tryng to determine a constant of variation that will satisfy the homogenous part

  24. amistre64
    • 5 years ago
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    i think

  25. amistre64
    • 5 years ago
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    B{n+1} - (1.015)B{n} = 0, or rather; B{n+1} = k* [1.015]B{n} and solve for k using the answers you found in the table

  26. anonymous
    • 5 years ago
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    I have something...checking to see if it works

  27. anonymous
    • 5 years ago
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    got it!

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