## 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).

1. anonymous

I have some it...just need some extra guidance

2. anonymous

\[b_{0} = 360 \]

3. anonymous

\[b_{n}=1.015b_{n-1} - 25 for n >0\]

4. anonymous

I have c at \$104.40

5. amistre64

B{0} = -360 right? since its debt?

6. anonymous

I would think it is just 360 applying debt as initial amount

7. amistre64

we can either look at it as the balance approaching zero from the left; or from the right i spose

8. anonymous

used positive for amortized problem and got that part right

9. amistre64

B{n+1} = B{n}(1.015) - 25 looks right for a recurence equation

10. anonymous

I have a chart so take from balance standpoint

11. amistre64

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

yes

13. anonymous

360(1.015)

14. amistre64

i really got no idea how to go from there ;)

15. anonymous

ok

16. amistre64

the general solution is the homogenous?

17. anonymous

yes

18. amistre64

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

I have 360, 340.4, 320.5, 300.3, 279.80, 259, 237.9...

20. amistre64

i always round up when working in money

21. amistre64

ack!!.. i did all that with 1.01 lol

22. amistre64

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

in general; you are tryng to determine a constant of variation that will satisfy the homogenous part

24. amistre64

i think

25. amistre64

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

I have something...checking to see if it works

27. anonymous

got it!