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).

Question

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).

anonymous · Answer

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

anonymous · Answer

$$b_{0} = 360 $$

anonymous · Answer

$$b_{n}=1.015b_{n-1} - 25     for n >0$$

anonymous · Answer

I have c at $104.40

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

anonymous · Answer

used positive for amortized problem and got that part right

amistre64 · Answer

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

anonymous · Answer

I have a chart so take from balance standpoint

amistre64 · Answer

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?

anonymous · Answer

yes

anonymous · Answer

360(1.015)

amistre64 · Answer

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

anonymous · Answer

ok

amistre64 · Answer

the general solution is the homogenous?

anonymous · Answer

yes

amistre64 · Answer

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?

anonymous · Answer

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

amistre64 · Answer

i always round up when working in money

amistre64 · Answer

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

amistre64 · Answer

there is a techniques refered to as variation of parameters that looks very close to this procedure... but i havent grasped it yet.

amistre64 · Answer

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

amistre64 · Answer

i think

amistre64 · Answer

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

anonymous · Answer

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

anonymous · Answer

got it!