Loan or Mortgage amortization function with Python

After some search on the internet, I'm not able to find a simple implementation of the loan or mortgage amortization schedule. This is usually achieved with the excel template in the financial world. One can simply use the formula to compute the monthly payment and the template to work on the schedule. There are more complex tasks that are not easily to refer to the excel sheet. For instance, we might want to perform a task to look up the balance on the amortization schedule to make the decision when to pay off the balance. This could be simply implemented in Python and it's a nice illustration of how to use Python in Finance. I decided to take a shot to the loan amortization function as the start of a financial calculator. The results has been cross checked with the financial calculators. 

There are generally tree steps. 

• Calculate the monthly payment for the loan
• Calculate the principle for amortization schedule
• Calculate the payment schedule

The monthly payment can be easily calculated with the following formula. The detailed loan amortization derivation can be found on wikipedia.

where

• A = payment amount per period
• P = initial principal (loan amount)
• r = interest rate per period
• n = total number of payments or periods

The first step is to calculate the monthly payment with the loan amortization formula. The input is the initial loan amount, the month interest and the total length of loan in months. The interest published is usually the nominal annual interest. The monthly interest can be simply derived by nominal interest/12. The Python function is listed as below.

def get_monthly_pmt(loan_amt, r, n):
    """ calculate monthly payment
    loan_amt: initial loan amount
    r: monthly interest
    n: total number of payments
    """
    return loan_amt*r*(1 + r)**n / ((1 + r)**n - 1)

"""
loan_amt = 500,000
r = 0.04/12
n = 300

>>> get_monthly_pmt(loan_amt=500000, r=0.04/12, n=300)

2639.1842014888507
"""

The second step is to calculate the principle of any month t.

def get_principle(loan_amt, A, r, t):
    """ calculate principle for month t
    loan_amt: intial loan amount
    A: monthly payment
    r: monthly intrest
    t: number of payments
    """
    return loan_amt*((1 + r)**t) - A*((1 + r)**t - 1)/r

The final step is to calculate the monthly amortization schedule. 

def get_schedule(loan_amt, r, n):
    """ calculate the amortization schedule
    loan_amt: intial loan amount
    r: monthly intrest
    n: total number of payments
    """
    monthly = []
    A = get_monthly_pmt(loan_amt, r, n)
    last = loan_amt
    for i in range(1, n+1):
        curr = get_principle(loan_amt, A, r, i)
        p = last - curr
        monthly.append([i, p, A - p, curr])
        last = curr
    return pd.DataFrame(monthly, columns=['month', 'principle_pmt', 'interest_pmt', 'principle'])

To put everything in the same place with a real time example. The output is a pandas data frame containing the amortization schedule. The balance of any month can be simply looked up from the data frame.

"""
Loan/Mortgage Amortization schedule
Financial calculator
"""

import pandas as pd


def get_monthly_pmt(loan_amt, r, n):
    """ calculate monthly payment
    loan_amt: initial loan amount
    r: monthly interest
    n: total number of payments
    """
    return loan_amt*r*(1 + r)**n / ((1 + r)**n - 1)
    

def get_principle(loan_amt, A, r, t):
    """ calculate principle for month t
    loan_amt: intial loan amount
    A: monthly payment
    r: monthly intrest
    t: number of payments
    """
    return loan_amt*((1 + r)**t) - A*((1 + r)**t - 1)/r

def get_schedule(loan_amt, r, n):
    """ calculate the amortization schedule
    loan_amt: intial loan amount
    r: monthly intrest
    n: total number of payments
    """
    monthly = []
    A = get_monthly_pmt(loan_amt, r, n)
    last = loan_amt
    for i in range(1, n+1):
        curr = get_principle(loan_amt, A, r, i)
        p = last - curr
        monthly.append([i, p, A - p, curr])
        last = curr
    return pd.DataFrame(monthly, columns=['month', 'principle_pmt', 'interest_pmt', 'principle'])

"""
loan_amt = 500,000
r = 0.04/12
n = 300

>>> get_monthly_pmt(loan_amt=500000, r=0.04/12, n=300)

2639.1842014888507

>>> df = show_schedule(loan_amt=500000, r=0.04/12, n=300)

month	principle_pmt	interest_pmt	principle
0	1	972.517535	1666.666667	499027.482465
1	2	975.759260	1663.424942	498051.723205
2	3	979.011791	1660.172411	497072.711414
3	4	982.275163	1656.909038	496090.436251
4	5	985.549414	1653.634788	495104.886837
...	...	...	...	...
295	296	2595.634264	43.549938	10469.347082
296	297	2604.286378	34.897824	7865.060704
297	298	2612.967332	26.216869	5252.093371
298	299	2621.677224	17.506978	2630.416148
299	300	2630.416148	8.768054	0.000000
"""