Loan Amortization Calculator Formula
Understand the math behind the loan amortization calculator. Each variable explained with a worked example.
Formulas Used
Monthly Payment
monthly_payment = monthly_rate > 0 ? loan_amount * monthly_rate * pow(1 + monthly_rate, num_payments) / (pow(1 + monthly_rate, num_payments) - 1) : loan_amount / num_paymentsTotal Amount Paid
total_paid = monthly_payment * num_paymentsTotal Interest Paid
total_interest = monthly_payment * num_payments - loan_amountFirst Month Interest
first_month_interest = loan_amount * monthly_rateFirst Month Principal
first_month_principal = monthly_payment - loan_amount * monthly_rateVariables
| Variable | Description | Default |
|---|---|---|
loan_amount | Loan Amount(USD) | 200000 |
annual_rate | Annual Interest Rate(%) | 6 |
loan_term_years | Loan Term(years) | 30 |
monthly_rate | Derived value= annual_rate / 12 / 100 | calculated |
num_payments | Derived value= loan_term_years * 12 | calculated |
How It Works
How Loan Amortization Works
Amortization is the process of spreading loan payments over time. Each payment covers interest on the remaining balance plus a portion of the principal.
Formula
Monthly Payment: M = P * [r(1+r)^n] / [(1+r)^n - 1]
For each payment:
Early payments are mostly interest; later payments are mostly principal.
Worked Example
A $200,000 loan at 6% interest for 30 years.
loan_amount = 200000annual_rate = 6loan_term_years = 30
- 01Monthly rate: 6% / 12 = 0.5% (0.005)
- 02Total payments: 30 * 12 = 360
- 03Monthly payment = $200,000 * [0.005 * (1.005)^360] / [(1.005)^360 - 1] = $1,199.10
- 04First month interest: $200,000 * 0.005 = $1,000.00
- 05First month principal: $1,199.10 - $1,000.00 = $199.10
- 06Total paid: $1,199.10 * 360 = $431,676.00
- 07Total interest: $431,676.00 - $200,000 = $231,676.00
Ready to run the numbers?
Open Loan Amortization Calculator