Comparing Loan Amortization Calculations Between Excel and Python with numpy_financial

Understanding the Variance in Loan Amortization Calculations

Loan amortization calculations might differ greatly based on the tools and methods employed. This article investigates the inconsistencies found while implementing French and Italian amortization systems in Python using the numpy_financial package vs findings obtained from Excel.

Despite utilizing the same conditions (interest rate, loan amount, length, and payment frequency), the results from Python computations differ from those from Excel. Understanding these variances is critical for creating realistic financial apps.

Command	Description
dateutil.relativedelta	Provides a method for computing relative deltas for date arithmetic, allowing for more flexible date calculations like adding months or years.
numpy_financial.pmt	Calculates the fixed payment required to fully amortize a loan over a specified number of periods, using a set interest rate.
numpy_financial.ipmt	Returns the interest part of a loan or investment payment for a certain period, assuming continuous monthly payments and an interest rate that remains constant.
numpy_financial.ppmt	Returns the principal component of a loan or investment payment for a particular term, using constant periodic payments and an interest rate that remains constant.
pandas.DataFrame	In Pandas, a two-dimensional labeled data structure is utilized to efficiently store and handle tabular data.
cumsum()	Computes the cumulative sum of array components, which is commonly used to generate running totals like the remaining loan debt after each payment.
dt.datetime.fromisoformat()	Parses a text expressing a date in ISO format and provides a datetime object for simple manipulation of date data.

Understanding Loan Amortization Calculation Discrepancies

The Python script given is intended to calculate loan amortization schedules using both French and Italian procedures. The script uses the library to calculate payment, interest, and principle amounts. The class is set up with parameters like interest rate, loan period, loan amount, amortization method, and payment frequency. The class determines the total number of payment periods using the method, which adapts based on the frequency: monthly, quarterly, semi-annual, or yearly. It also computes the period-specific interest rate using the calculate_period_rate technique. The payment amount is calculated using , which determines the fixed payment amount needed to amortize the loan over the specified period.

Method creates the amortization schedule. It generates a list of payment dates based on the payment frequency and a table with payment, interest, and principle amounts. The French amortization technique employs to calculate the interest component of each payment, and to calculate the principal portion. These numbers are then integrated into a Pandas DataFrame, allowing for easy manipulation and visualization. The Italian technique uses a script that calculates interest as a fixed percentage of the remaining loan balance and principle as a fixed sum. This schedule is also stored as a Pandas DataFrame. Despite the right implementation, inconsistencies appear when comparing the Python results to those from Excel, as the PMT function returns various payment values under identical situations.

import datetime as dt
from dateutil.relativedelta import relativedelta
import numpy_financial as npf
import pandas as pd

class Loan:
    def __init__(self, rate, term, loan_amount, amortization_type, frequency, start=dt.date.today().isoformat()):
        self.rate = rate
        self.term = term
        self.loan_amount = loan_amount
        self.start = dt.datetime.fromisoformat(start).replace(day=1)
        self.frequency = frequency
        self.periods = self.calculate_periods()
        self.period_rate = self.calculate_period_rate()
        self.pmt = npf.pmt(self.period_rate, self.periods, -self.loan_amount)
        self.amortization_type = amortization_type
        self.table = self.loan_table()

    def calculate_periods(self):
        if self.frequency == 'monthly':
            return self.term * 12
        elif self.frequency == 'quarterly':
            return self.term * 4
        elif self.frequency == 'semi-annual':
            return self.term * 2
        elif self.frequency == 'annual':
            return self.term
        else:
            raise ValueError("Unsupported frequency")

    def calculate_period_rate(self):
        if self.frequency == 'monthly':
            return self.rate / 12
        elif self.frequency == 'quarterly':
            return self.rate / 4
        elif self.frequency == 'semi-annual':
            return self.rate / 2
        elif self.frequency == 'annual':
            return self.rate
        else:
            raise ValueError("Unsupported frequency")

=PMT(4.5%/1, 10*1, -1500000)
=IPMT(4.5%/1, A2, 10*1, -1500000)
=PPMT(4.5%/1, A2, 10*1, -1500000)
=A2-P2
for each period

def loan_table(self):
    if self.frequency == 'monthly':
        periods = [self.start + relativedelta(months=x) for x in range(self.periods)]
    elif self.frequency == 'quarterly':
        periods = [self.start + relativedelta(months=3*x) for x in range(self.periods)]
    elif self.frequency == 'semi-annual':
        periods = [self.start + relativedelta(months=6*x) for x in range(self.periods)]
    elif self.frequency == 'annual':
        periods = [self.start + relativedelta(years=x) for x in range(self.periods)]
    else:
        raise ValueError("Unsupported frequency")

    if self.amortization_type == "French":
        interest = [npf.ipmt(self.period_rate, month, self.periods, -self.loan_amount, when="end") for month in range(1, self.periods + 1)]
        principal = [npf.ppmt(self.period_rate, month, self.periods, -self.loan_amount) for month in range(1, self.periods + 1)]
        table = pd.DataFrame({'Payment': self.pmt, 'Interest': interest, 'Principal': principal}, index=pd.to_datetime(periods))
        table['Balance'] = self.loan_amount - table['Principal'].cumsum()
    elif self.amortization_type == "Italian":
        interest = [self.loan_amount * self.period_rate]
        principal_payment = self.loan_amount / self.periods
        principal = [principal_payment]
        payment = [interest[0] + principal[0]]
        for month in range(1, self.periods):
            interest_payment = (self.loan_amount - (month) * principal_payment) * self.period_rate
            interest.append(interest_payment)
            principal.append(principal_payment)
            payment.append(interest_payment + principal_payment)

        principal[-1] = self.loan_amount - sum(principal[:-1])
        payment[-1] = interest[-1] + principal[-1]

        table = pd.DataFrame({'Payment': payment, 'Interest': interest, 'Principal': principal}, index=pd.to_datetime(periods))
        table['Balance'] = self.loan_amount - table['Principal'].cumsum()
    else:
        raise ValueError("Unsupported amortization type")
    return table.round(2)

Examining Interest Calculation Differences in Loan Amortization

The way interest is compounded and managed over time is a significant factor in the disparities between Python and Excel calculations. Excel's , , and functions use a specific compounding approach that aligns with financial industry norms. However, when same computations are repeated in Python using the numpy_financial library, minor variations in the handling of interest accrual and rounding can result in different results. Understanding these distinctions is critical for maintaining consistency across platforms.

Furthermore, discrepancies in the underlying methods utilized by Python and Excel can cause disparities in amortization timelines. Excel's functions are designed for quick, accurate computations, however they may employ approximations that differ from Python's more detailed calculations. The Python script provides a class structure to define loan parameters and methods for calculating the amortization plan. This provides for greater flexibility and customization, but it also necessitates meticulous handling of each computation step to avoid errors. To achieve consistent results, both platforms must use the same compounding frequency, interest computation methodologies, and rounding standards.

1. Why are my Python and Excel amortization schedules different?
2. Errors can occur due to variations in compounding methods, interest calculating practices, and rounding errors. Maintaining consistency in these areas is critical.
3. What is the use of the library in loan calculations?
4. offers financial functions such as , , and PPMT to calculate payments, interest, and principal for loans and investments.
5. How can I verify that my Python findings match those in Excel?
6. Check that the compounding frequency, interest rates, and rounding procedures are consistent in Python and Excel.
7. What does the function accomplish?
8. The function computes the fixed payment needed to fully amortize a loan over a specified number of periods at a constant interest rate.
9. Why does compounding frequency matter?
10. Compounding frequency influences how interest is computed, which can have a substantial impact on total payment amount and amortization timeline.
11. What is the distinction between the French and Italian amortization methods?
12. French amortization uses constant payments with fluctuating principal and interest percentages, whereas Italian amortization uses fixed principal payments with decreasing interest amounts.
13. How does the function affect amortization schedules?
14. The function computes the cumulative total, which helps determine the outstanding loan debt after each payment.
15. Can rounding disparities influence loan calculations?
16. Yes, even minor rounding variations might result in noticeable variances over time. Consistent rounding techniques are crucial.
17. What are the and functions used for?
18. computes the interest portion of a payment, whereas computes the principle portion of a loan for a specific term.

Addressing the differences between loan amortization computations in Python and Excel necessitates a thorough grasp of the underlying mechanisms employed by each platform. Matching outcomes can be achieved by using consistent compounding frequencies, interest computation processes, and rounding approaches. This investigation emphasizes the significance of rigorous attention to detail in financial computations in order to assure accuracy and reliability across multiple tools and software.