"""
Ex A.4 from "A primer on..." 
Compute the value of a loan of size L
which is paid back over N months, and
also the monthly payment, by solving
a system of two differential equations.
"""

import numpy as np
import matplotlib.pyplot as plt

L = 100                      # initial amount
p = 5                         # interest rate
N = 40                        # number of months

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

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

for n in months[1:]:
    y[n] = (p/(12 * 100)) * x[n-1] + L/N
    x[n] = x[n-1] + (p/(12* 100.0)) * x[n-1] - y[n]


plt.plot(months, y, 'bx')
plt.xlabel('Months')
plt.ylabel('Amount')
plt.show()

"""
Terminal> python loan.py 
(output is a plot)
"""