"""
Exercise A.4. Very similar to the
interest_rate example from the slides/book,
but we solve a system of two difference equations,
ending up with two arrays:
x - the remaining loan after month n
y - the amount we pay in month n
"""

from numpy import *
from matplotlib.pyplot import *

L = 100
p = 5
N = 36 #months

index_set = range(N+1)
x = zeros(len(index_set))
y = zeros_like(x)   #alternatively y = zeros(len(index_set))

x[0] = L
y[0] = 0

for n in index_set[1:]:
    y[n] = x[n-1]*p/(12*100) + L/N
    x[n] = x[n-1] + x[n-1]*p/(12*100) - y[n]

#plot x as red circles, y as blue +
plot(x,'ro')
plot(y,'b+')
show()