Calculating a Loan Balance Over Time

import datetime as dt
import pandas as pd

def loan(date, balance, rate, payment, payment_day):
    day_list = [(date, balance, 0, 0, 0, 0)]

    while day_list[-1][1] > 0:
        date               = day_list[-1][0]
        principal          = day_list[-1][1]
        interest           = day_list[-1][2]
        cum_paid_interest  = day_list[-1][4]
        cum_paid_principal = day_list[-1][5]

        new_principal = principal
        new_interest  = interest + principal * rate / 365
        new_date      = date + dt.timedelta(1)

        if new_date.day == payment_day:
            if new_principal - (payment - new_interest) > 0:
                paid_principal = payment - new_interest
            else:
                paid_principal = new_principal
                
            new_principal      -= paid_principal
            cum_paid_interest  += new_interest
            cum_paid_principal += paid_principal
            
            if payment > new_interest:
                new_interest = 0
            else:
                new_interest -= payment
        else:
            paid_principal = 0

        day_list.append((new_date, new_principal, 
                         new_interest, paid_principal, 
                         cum_paid_interest, cum_paid_principal))
    d = pd.DataFrame(day_list,
                     columns=['date', 'principal', 'interest', 
                              'paid_principal', 'cum_paid_interest', 
                              'cum_paid_principal'])
    d['date'] = pd.to_datetime(d['date'])
    return d

start_date  = dt.date(2000,1,1)
balance     = 250000
annual_rate = 0.035
payment     = 1787
payment_day = 1

daily = loan(start_date, balance, annual_rate, payment, payment_day)
daily.head(10)

payment_days_only = (daily[(daily['paid_principal']!=0)|
                           (daily.index==0)]
                     .reset_index(drop=True))
payment_days_only.head()

payment_days_only.tail()

import matplotlib.pyplot as plt

def create_loan_payoff_plot(d):
    fig = plt.figure(figsize=[11,8.5])
        
    ax = fig.gca()    
    ax.grid(True)
    
    ax.spines['left'].set_visible(False)
    ax.spines['top'].set_visible(False)
    ax.spines['right'].set_visible(False)
    ax.spines['bottom'].set_visible(False)
    
    plt.tick_params(
        axis='y',
        left=False)
    plt.tick_params(
        axis='x',
        bottom=False)
    
    plt.title('$250K, 15-Year Mortgage, $1787 Payment')
        
    ax.plot(d['date'],
            d['principal'] + d['interest'],
            linewidth=1,
            label='Loan Balance')
    
    ax.plot(d['date'],
            d['cum_paid_principal'],
            linewidth=1,
            label='Equity')
    
    ax.plot(d['date'],
            d['cum_paid_interest'],
            linewidth=1,
            label='Cumulative Paid Interest')
    
    ax.legend()
create_loan_payoff_plot(daily)

payment_days_only[payment_days_only['date'].dt.month==1]