# Setting up the initial packages necessary for
# this script
import numpy as np
import matplotlib.pyplot as plt
import locale
%matplotlib inline

locale.setlocale(locale.LC_ALL,'')
# This is so that any money displayed on the
# output plot is in dollars, separated by
# commas per three digits

def compoundInt(principal,rate,years,contr,compounded='monthly'):
    # This is where the magic happens
    # This function takes in: 
    #    the principal amount in dollars
    #    the APY interest rate in x%
    #    the number of years of in question
    #    the amount contributed per compounding period
    #    how often interest is compounded per year; default is monthly
    #
    # This function then returns:
    #    the array for the amount of money accumulated at each compounding period
    #    the array for the amount of money deposited at each compounding period

    if compounded == 'monthly':
        N_comp = 12.
    elif compounded == 'daily':
        N_comp = 365.
    elif compounded == 'weekly':
        N_comp = 52.
    elif compounded == 'quarterly':
        N_comp = 4.
    elif compounded == 'semi-annually':
        N_comp = 2.
    elif compounded == 'annually':
        N_comp = 1.
    
    rate = rate/100.
    N = int(years*N_comp) # the number of compounding periods total
    tot = np.zeros(N + 1) # array that will contain the total amount
                          # of money accrued over time from both
                          # deposits and interest
    tot[0] = principal
    deposits = np.zeros(N + 1) # array that will contain the total
                               # amount of money deposited over time
    deposits[0] = principal
    for i in range(N):
        # Formula for compound interest with deposits
        # Compound Interest Formula: A_comp = principal * ((1 + rate/N_comp)**(i+1 periods))
        # Added Value from Contributions: A_contr = contr * ((1 + rate/N_comp)**(i+1 periods)-1.)/(rate/N_comp)
        # Total: tot[i+1] = A_comp + A_contr
        #
        # Deposits to-date: deposits[i+1] = deposits[i] + contr 
        tot[i+1] = ((1+rate/N_comp)**(i+1))*tot[0] + contr*((1 + rate/N_comp)**(i+1)-1.)/(rate/N_comp)
        deposits[i+1] = deposits[i] + contr 
    return tot,deposits

## These are going to be your input values
## Nyrs -- The number of years over which your investment grows
##
## rates -- Array of interest rates that you want to compare, in percents.
##          Note: You don't need three. You can have as many as
##          you want.  However, three is what I plot with
##
## princ -- The principal investment in dollars
##
## contr -- Your monthly contribution, in dollars

Nyrs = 40.
rates = [10.,7.,4.] # 
princ = 0.
contr = 450.

## This is where the calculation occurs.  You need one set of
## these lines for each rate you want to examine

p_hi, amt = compoundInt(princ,rates[0],Nyrs,contr)
intrst_hi = p_hi[1:]-p_hi[:-1] - contr

p_avg, amt = compoundInt(princ,rates[1],Nyrs,contr)
intrst_avg = p_avg[1:]-p_avg[:-1] - contr

p_lo, amt = compoundInt(princ,rates[2],Nyrs,contr)
intrst_lo = p_lo[1:]-p_lo[:-1] - contr

## All of the plotting.  If you didn't change anything above,
## just hit Control+Enter

yrs = np.linspace(0,Nyrs,int(Nyrs*12)+1)
fig = plt.figure(figsize=(8,9))
fig.subplots_adjust(hspace=0)
plt.suptitle('Principal - '+locale.currency(princ, grouping=True)+'\n Monthly Contribution - '+locale.currency(contr)+'\n Time - %i Years' % Nyrs+'\n Total Contribution - '+locale.currency(amt[-1], grouping=True))
ax = plt.subplot2grid((2,1),(0,0))
ax.fill_between(yrs,p_hi/1.0E3,p_avg/1.0E3,alpha=0.5,color='g')
ax.fill_between(yrs,p_avg/1.0E3,p_lo/1.0E3,alpha=0.5,color='r')
ax.plot(yrs,p_hi/1.0E3,color='g',linewidth=2)
ax.plot(yrs,p_lo/1.0E3,color='r',linewidth=2)
ax.plot(yrs,p_avg/1.0E3,color='k',linewidth=2)

ax.plot([0,41],[p_hi[-1]/1.0E3,p_hi[-1]/1.0E3],linestyle='--',color='g')
ax.plot([0,41],[p_lo[-1]/1.0E3,p_lo[-1]/1.0E3],linestyle='--',color='r')
ax.plot([0,41],[p_avg[-1]/1.0E3,p_avg[-1]/1.0E3],linestyle='--',color='k')

ax.text(2,p_hi[-1]/1000.-.05*(p_hi[-1]/1000.),locale.currency(p_hi[-1], grouping=True) + ' (10% Interest)')
ax.text(2,p_avg[-1]/1000.-.05*(p_hi[-1]/1000.),locale.currency(p_avg[-1], grouping=True) + ' (7% Interest)')
ax.text(2,p_lo[-1]/1000.-.05*(p_hi[-1]/1000.),locale.currency(p_lo[-1], grouping=True) + ' (4% Interest)')
ax.minorticks_on()
ax.set_xlabel('Years')
ax.set_xlim(1,Nyrs)
ax.set_ylim(0,max(p_hi/1000.)+.1*(p_hi[-1]/1000.))
ax.set_ylabel('Investment Values (x $1000)')

ax = plt.subplot2grid((2,1),(1,0))
ax.fill_between(yrs[1:],intrst_avg/1.0E3,intrst_hi/1.0E3,alpha=0.5,color='g')
ax.fill_between(yrs[1:],intrst_lo/1.0E3,intrst_avg/1.0E3,alpha=0.5,color='r')
ax.plot(yrs[1:],intrst_hi/1.0E3,c='g',linewidth=2)
ax.plot(yrs[1:],intrst_lo/1.0E3,c='r',linewidth=2)
ax.plot(yrs[1:],intrst_avg/1.0E3,c='k',linewidth=2)
ax.minorticks_on()
ax.set_xlabel('Years')
ax.set_ylabel('Interest Value (x $1000)')
ax.set_xlim(1,Nyrs)
ax.set_ylim(0,max(intrst_hi/1.0E3))
plt.show()

## This cell shows you how many years and months 
## it would take for your interest to exceed
## your principal investment

mask_hi = np.where(p_hi-amt > amt)[0]
print 'Amount gained from an interest rate of %.2f%%\n\t...%s\nis more than the amount deposited after %i years and %.1f months\n\t...%s\n' % (rates[0],locale.currency(p_hi[mask_hi[0]]-amt[mask_hi[0]], grouping=True),int(yrs[mask_hi[0]]),(yrs[mask_hi[0]]-int(yrs[mask_hi[0]]))*12,locale.currency(amt[mask_hi[0]], grouping=True))

mask_avg = np.where(p_avg-amt > amt)[0]
print 'Amount gained from an interest rate of %.2f%%\n\t...%s\nis more than the amount deposited after %i years and %.1f months\n\t...%s\n' % (rates[1],locale.currency(p_avg[mask_avg[0]]-amt[mask_avg[0]], grouping=True),int(yrs[mask_avg[0]]),(yrs[mask_avg[0]]-int(yrs[mask_avg[0]]))*12,locale.currency(amt[mask_avg[0]], grouping=True))

mask_lo = np.where(p_lo-amt > amt)[0]
print 'Amount gained from an interest rate of %.2f%%\n\t...%s\nis more than the amount deposited after %i years and %.1f months\n\t...%s\n' % (rates[2],locale.currency(p_lo[mask_lo[0]]-amt[mask_lo[0]], grouping=True),int(yrs[mask_lo[0]]),(yrs[mask_lo[0]]-int(yrs[mask_lo[0]]))*12,locale.currency(amt[mask_lo[0]], grouping=True))

## All of the plotting.  If you didn't change anything above,
## just hit Control+Enter

yrs = np.linspace(0,Nyrs,int(Nyrs*12)+1)

fig = plt.figure(figsize=(10,7))
fig.subplots_adjust(hspace=0)
ax = plt.subplot2grid((1,1),(0,0))
ax.fill_between(yrs,p_hi/1.0E3,p_avg/1.0E3,alpha=0.5,color='g')
ax.fill_between(yrs,p_avg/1.0E3,p_lo/1.0E3,alpha=0.5,color='r')
ax.plot(yrs,p_hi/1.0E3,color='g',linewidth=2)
ax.plot(yrs,p_lo/1.0E3,color='r',linewidth=2)
ax.plot(yrs,p_avg/1.0E3,color='k',linewidth=2)

ax.plot([0,41],[p_hi[-1]/1.0E3,p_hi[-1]/1.0E3],linestyle='--',color='g')
ax.plot([0,41],[p_lo[-1]/1.0E3,p_lo[-1]/1.0E3],linestyle='--',color='r')
ax.plot([0,41],[p_avg[-1]/1.0E3,p_avg[-1]/1.0E3],linestyle='--',color='k')

growth_hi = (p_hi[-1]-amt[-1])/amt[-1] * 100.
growth_avg = (p_avg[-1]-amt[-1])/amt[-1] * 100.
growth_lo = (p_lo[-1]-amt[-1])/amt[-1] * 100.


ax.text(2,p_hi[-1]/1000.-.05*(p_hi[-1]/1000.),locale.format("%d",growth_hi, grouping=True) + '% growth at 10% Interest')
ax.text(2,p_avg[-1]/1000.-.05*(p_hi[-1]/1000.),locale.format("%d",growth_avg, grouping=True) + '% growth at 7% Interest')
ax.text(2,p_lo[-1]/1000.-.05*(p_hi[-1]/1000.),locale.format("%d",growth_lo, grouping=True) + '% growth at 4% Interest')
ax.minorticks_on()
ax.set_xlim(1,Nyrs)
ax.set_ylim(0,max(p_hi/1000.)+.1*(p_hi[-1]/1000.))

plt.show()

print amt[-1]
print p_hi[-1]
growth_hi = (p_hi[-1]-amt[-1])/amt[-1] * 100.
print growth_hi

compoundInt(100,10,50,0,compounded='monthly')[0][10]