"""
Example from lectures 29 sept-01 oct. The simplest
example of a difference equation, modeling how an
invested amount grows over time.
"""


import matplotlib.pyplot as plt
import numpy as np

x0 = 100 # initial amount
p = 5 # interest rate
N = 4 # number of years
years = list(range(N+1))

x = np.zeros(len(years))

# Compute solution
x[0] = x0
for i in years[1:]:
    x[i] = x[i-1] + (p/100.0) * x[i-1]

plt.plot(years, x, 'ro')
plt.xlabel('years') 
plt.ylabel('amount')
plt.show()