# Exercise A.4

# A.16: y_n = p/(12*100)*x_n-1 + L/N
# A.17: x_n = x_n-1 + p/(12*100)*x_n-1 - y_n
# Initial condition: x_0 = L
# x_n = value of loan after month n
# y_n = payment in month n

import numpy as np

def value_payment(L, p, N):
	x = np.zeros(N+1)
	y = np.zeros(N+1)
	x[0] = L
	for n in range(1,N+1):
		y[n] = float(p)/(12*100)*x_[n-1] + float(L)/N
		x[n] = x[n-1] + float(p)/(12*100)*x[n-1] - y[n]
	return x, y

"""
# Laan paa 1000 kr, aarlig rente 10 prosent, 12 mnd 
# tilbakebetalingstid
x, y = value_payment(1000, 10, 12)
print("Month    Payment     Loan after month")
for k in range(len(x)):
    print("%d     %f     %f" % (k, y[k], x[k]))
"""