Mortgage Loan Calculator & Amortization | Interactive Finance Math

Mortgage assumptions

Property price ($) Down payment ($) Annual interest rate (%) Loan term (years)

Loan balance Cumulative interest paid Cumulative principal repaid

Mortgage loan amount—

Monthly repayment—

Total of all payments—

Total interest paid—

Down payment—

Loan-to-value (LTV)—

Year	Opening Balance	Payments	Principal	Interest	Closing Balance

What to investigate: Increase the interest rate and observe the monthly payment and total interest. Then shorten the mortgage term. A shorter term usually increases the monthly repayment but can dramatically reduce the total interest paid. The table summarizes the amortization by year rather than displaying hundreds of monthly rows.

Explore Mortgage Amortization

The mortgage payment is chosen so that the present value of all future monthly repayments equals the amount borrowed. Each month, interest is charged on the remaining balance and the rest of the payment reduces the principal.

Use the Python model to generate the same amortization schedule and compare it with the interactive calculator.

import numpy as np

# Mortgage assumptions
property_price = 500000
down_payment = 100000
annual_rate = 0.045
loan_years = 30

# Amount borrowed
principal = (
    property_price - down_payment
)

monthly_rate = annual_rate / 12
number_payments = loan_years * 12

# Monthly mortgage payment
if monthly_rate == 0:
    payment = (
        principal / number_payments
    )
else:
    payment = principal * (
        monthly_rate
        * (1 + monthly_rate)
        ** number_payments
    ) / (
        (1 + monthly_rate)
        ** number_payments - 1
    )

print(
    "Loan amount:",
    round(principal, 2)
)

print(
    "Monthly payment:",
    round(payment, 2)
)

# Build amortization schedule
balance = principal
total_interest = 0

for month in range(
    1, number_payments + 1
):
    interest = (
        balance * monthly_rate
    )

    principal_paid = (
        payment - interest
    )

    # Avoid a tiny rounding balance
    if principal_paid > balance:
        principal_paid = balance

    balance -= principal_paid
    total_interest += interest

    if month % 12 == 0:
        print(
            "Year",
            month // 12,
            "Balance:",
            round(balance, 2)
        )

total_payments = (
    principal + total_interest
)

print()
print(
    "Total interest:",
    round(total_interest, 2)
)

print(
    "Total mortgage payments:",
    round(total_payments, 2)
)

loan_to_value = (
    principal / property_price * 100
)

print(
    "Loan-to-value:",
    round(loan_to_value, 2),
    "%"
)

Mortgage Loan Python Model

This model applies the standard amortizing-loan formula and then simulates the mortgage month by month. Compare different interest rates and loan terms to see why the borrowing cost can change substantially even when the original loan amount is unchanged.