Finance & Economics · Real Estate & Mortgages · Mortgage Calculations
Amortization Schedule Calculator
Calculates the fixed monthly payment, total interest paid, and full amortization breakdown for any fixed-rate loan.
Calculator
Formula
M is the fixed monthly payment. P is the loan principal (the amount borrowed). r is the monthly interest rate, calculated as the annual interest rate divided by 12. n is the total number of monthly payments, equal to the loan term in years multiplied by 12. Each month, interest accrues on the remaining balance, and the remainder of M reduces the principal — a process that repeats until the balance reaches zero.
Source: Standard actuarial annuity formula; see also Fabozzi, F.J. — Fixed Income Mathematics, 4th Edition (McGraw-Hill, 2006).
How it works
What is loan amortization? Amortization is the process of paying off a debt through scheduled, fixed periodic payments. Each payment covers two components: interest on the outstanding balance and a portion that reduces the principal. In the early months of a loan, the vast majority of each payment goes toward interest because the outstanding balance is at its highest. As the balance decreases over time, each successive payment allocates progressively more to principal and less to interest — a pattern that defines the amortization curve.
The formula in depth: The monthly payment M is derived from the present value of an ordinary annuity. Given a principal P, a monthly interest rate r (annual rate divided by 12), and n total monthly payments (years × 12), the formula is M = P × [r(1+r)^n] / [(1+r)^n − 1]. The numerator scales the principal by the compound growth of the rate, while the denominator represents the total discount factor across all payments. Multiplying M by n gives the total amount repaid, and subtracting P from that figure yields the total interest cost — often a startling number for long-term loans.
Practical context: For a 30-year mortgage at a moderate interest rate, total interest paid routinely exceeds 80–100% of the original loan balance. This is why shorter loan terms and extra principal payments can save tens of thousands of dollars. The amortization calculator is commonly used to compare a 15-year versus 30-year mortgage, assess the impact of a larger down payment, evaluate whether to refinance, and model accelerated payoff scenarios by applying lump-sum payments. Financial advisors also use it when counseling clients on debt management and net worth optimization.
Worked example
Suppose you take out a $300,000 mortgage at an annual interest rate of 6.5% for a term of 30 years.
Step 1 — Convert the annual rate to a monthly rate:
r = 6.5% ÷ 12 = 0.065 ÷ 12 ≈ 0.005417 per month
Step 2 — Calculate total number of payments:
n = 30 × 12 = 360 monthly payments
Step 3 — Apply the amortization formula:
M = 300,000 × [0.005417 × (1.005417)^360] / [(1.005417)^360 − 1]
(1.005417)^360 ≈ 6.8485
M = 300,000 × [0.005417 × 6.8485] / [6.8485 − 1]
M = 300,000 × [0.037101] / [5.8485]
M = 300,000 × 0.006341 ≈ $1,896.20 per month
Step 4 — Calculate total amount paid and total interest:
Total Paid = $1,896.20 × 360 = $682,632
Total Interest = $682,632 − $300,000 = $382,632
Step 5 — First month's amortization breakdown:
Interest portion (Month 1) = $300,000 × 0.005417 = $1,625.00
Principal portion (Month 1) = $1,896.20 − $1,625.00 = $271.20
Remaining balance = $300,000 − $271.20 = $299,728.80
This illustrates how in the very first payment, over 85% of the payment is pure interest. The ratio gradually shifts until the final payments are almost entirely principal.
Limitations & notes
This calculator assumes a fixed interest rate throughout the loan term. Adjustable-rate mortgages (ARMs) will have different payment trajectories after the initial fixed period and require a more complex model that accounts for rate resets. The formula also assumes payments are made on a strict monthly schedule with no missed payments, no extra principal payments, and no prepayment penalties — all of which would alter both the schedule and the total interest paid. Additionally, this tool does not account for ancillary costs that affect the true cost of a mortgage, including property taxes, homeowners insurance, private mortgage insurance (PMI), or origination fees. For interest-only loans, balloon mortgages, or loans with irregular payment structures, this standard annuity formula does not apply. Always consult a licensed mortgage professional or financial advisor before making major borrowing decisions, as real loan agreements may include fees and conditions not captured here.
Frequently asked questions
What is an amortization schedule and why does it matter?
An amortization schedule is a complete table showing every monthly payment over the life of a loan, broken down into its principal and interest components. It matters because it reveals the true cost of borrowing — for a $300,000 mortgage at 6.5% over 30 years, you end up paying over $382,000 in interest alone, more than the original loan amount. Understanding this helps borrowers make informed decisions about loan terms and extra payments.
Why does so much of my early mortgage payment go toward interest?
In the early months, the outstanding loan balance is at its maximum, so interest accrues on a large principal. For a $300,000 loan at 6.5%, the first month's interest alone is $1,625 out of an $1,896 payment — about 86%. As you pay down the balance, interest shrinks and principal grows. This front-loading of interest is a fundamental property of any fixed-payment amortizing loan, not a trick by lenders.
How much do I save by choosing a 15-year mortgage over a 30-year mortgage?
On a $300,000 loan at 6.5%, a 30-year term costs approximately $382,600 in total interest. The same loan on a 15-year term at 6.0% (rates are typically lower for 15-year loans) would cost roughly $155,500 in interest — a saving of over $220,000. However, the monthly payment rises from about $1,896 to roughly $2,532, so affordability and cash flow must be weighed against the long-term savings.
What happens if I make extra principal payments?
Extra principal payments reduce your outstanding balance faster, which means less interest accrues in subsequent months. Even one additional principal payment per year can shave several years off a 30-year mortgage and save tens of thousands in interest. Because this calculator assumes a fixed schedule, use it as a baseline — then model extra payments separately by recalculating with a shorter effective term or a lower remaining balance.
Does this formula work for auto loans and personal loans, not just mortgages?
Yes. The same fixed-payment amortization formula applies to any fully amortizing installment loan, including auto loans, personal loans, and student loans, as long as the interest rate is fixed and payments are made monthly. Simply enter the loan principal, annual rate, and term in years (e.g., 5 years for a car loan) and the calculator will return the correct monthly payment and total interest figures.
Last updated: 2025-01-15 · Formula verified against primary sources.