"""
Exercise A.4 from "A primer on...
Solve a system of diff. eqs describing
the evolution of a loan. 
"""


import numpy as np
import matplotlib.pyplot as plt

N = 25 * 12
L = 5e6
p = 5.0

x = np.zeros(N+1)
y = np.zeros(N+1)

months = range(N + 1)

x[0] = L

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

#plt.plot(months, x)
plt.plot(months, y)
plt.show()