import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
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We study the temporal evolution of an initial investment (or pricipal) of P dollars at an annual interest rate r for 24 months. We consider simple and compounded interest with a different number of compoundings per year.
#Principal
P = 1000
#Annual interest rate (decimal)
r = 0.10
#Number of compounds per year
compounds_per_year = [4,6]
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def future_value(t,n):
return P * (1 + r/n)^np.floor(t/12*n)
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def simple_future_value(t):
return P*(1 + r*np.floor(t/12))
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fig = plt.figure()
axes= fig.add_subplot(111)
x = np.linspace(0,24,500)
colors = ['blue']
n = 4 #copounds_per_year
z = simple_future_value(x)
y = future_value(x,n)
axes.plot(x,z,linewidth=2,color='black',label='simple')
text = 'n=' + str(n)
#axes.plot(x,y,linewidth=2,color=colors[0],label=text)
plt.legend(loc=2)
plt.xlabel('Months')
plt.ylabel('Dollars')
fig.savefig('test.png')
plt.close()
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fig = plt.figure()
axes= fig.add_subplot(111)
x = np.linspace(0,24,500)
colors = ['blue']
n = 6 #copounds_per_year
z = simple_future_value(x)
y = future_value(x,n)
#axes.plot(x,z,linewidth=2,color='blue',label='n')
text = 'n=' + str(n)
axes.plot(x,y,linewidth=2,color=colors[0],label=text)
plt.legend(loc=2)
plt.xlabel('Months')
plt.ylabel('Dollars')
fig.savefig('test.png')
plt.close()
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fig = plt.figure()
axes= fig.add_subplot(111)
x = np.linspace(0,24,500)
colors = ['red','blue','black']
z = simple_future_value(x)
axes.plot(x,z,linewidth=2,color='black',label='simple')
for k,n in enumerate(compounds_per_year):
y = future_value(x,n)
text = 'n=' + str(n)
axes.plot(x,y,linewidth=2,color=colors[k],label=text)
plt.legend(loc=2)
plt.xlabel('Months')
plt.ylabel('Dollars')
fig.savefig('test.png')
plt.close()
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fig = plt.figure()
axes= fig.add_subplot(111)
#compounds_per_year = [2,1000]
x = np.linspace(0,24,500)
y = future_value(x,compounds_per_year[1])-future_value(x,compounds_per_year[0])
text = 'n='+str(compounds_per_year[1]) + ' minus ' + 'n='+str(compounds_per_year[0])
axes.plot(x,y,linewidth=2,label=text)
plt.legend(loc=2)
plt.xlabel('Months')
plt.ylabel('Dollars')
fig.savefig('test.png')
plt.clf()
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o = [1]*11
alignment = 0
x = np.arange(0,11,1)+alignment
x = np.array(x,dtype=np.float64)
y = [49,58,66,72,76,79,80,80,78,74,69]
y = np.array(y,dtype=np.float64)
y = y.transpose()
w = np.array([x,y])
print w.transpose()
fig = plt.figure()
axes = fig.add_subplot(111)
axes.plot(x,y,'ko')
plt.xlabel('Time (hours after 7 am)')
plt.ylabel('Temperature ($^\circ$F)')
#----------------------------------------
m = np.array([o,x,x^2])
m = m.transpose()
U,s,V = np.linalg.svd(m,full_matrices=False)
b = U.transpose().dot(y)
s = 1/s
z = s * b
x = V.transpose().dot(z)
print x
#----------------------------------------
def temp_fun(t):
return x[0] + x[1] * t + x[2] * t**2
#----------------------------------------
t = np.linspace(0,10,500)+alignment
axes.plot(t,temp_fun(t),linewidth=2,color='red')
#----------------------------------------
fig.savefig('test.png')
plt.close()
[[ 0. 49.] [ 1. 58.] [ 2. 66.] [ 3. 72.] [ 4. 76.] [ 5. 79.] [ 6. 80.] [ 7. 80.] [ 8. 78.] [ 9. 74.] [ 10. 69.]] [ 48.97202797 10.01864802 -0.8018648 ] [[ 0. 49.] [ 1. 58.] [ 2. 66.] [ 3. 72.] [ 4. 76.] [ 5. 79.] [ 6. 80.] [ 7. 80.] [ 8. 78.] [ 9. 74.] [ 10. 69.]] [ 48.97202797 10.01864802 -0.8018648 ] 
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#Choose a model
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