Let an be the amount on a credit card that charges 1.5% interest each month. Suppose, a person pay $50 each month, then the dynamical system as follows:
The equilibrium value for the dynamical system is
an+1=ran+b, r=1
Here, an+1=an+0.015an−50
whith a0=500
For, n=0
a1=a0+0.015a0−50
a1=500+0.015(500)−50=457.5
For n=1
a2=a1+0.015a1−50
a2=457.5+0.015(457.5)−50=414.3625
a3=a2+0.015a2−50
a3=414.3625+0.015(414.3625)−50=370.5779
a4=a3+0.015a3−50
a4=370.5779+0.015(370.5778)−50=326.1366
a5=a4+0.015a4−50
a5=326.1366+0.015(326.1366)−50=281.0287
a6=a5+0.015a5−50
a6=281.0287+0.015(281.0281)−50=235,2441
a7=a6+0.015a6−50
a7=235,2441+0.015(235,2441)−50=188.7727
a8=a7+0.015a7−50
a8=188.7727+0.015(188.7727)−50=141.6043
a9=a8+0.015a8−50
a9=141.6043+0.015(141.6043)−50=93.7284
a10=a9+0.015a9−50
a10=93.7284+0.015(93.7284)−50=45.1343
a11=a10+0.015a10−50
a11=45.1343+0.015(45.1343)−50=−4.1887
Account will be paid off for 11 months.
Last payment will be 50-4.19=45.81
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