About the Amortization Calculator
An amortization calculator generates the full payment schedule for an amortizing loan — mortgage, auto loan, student loan, or any installment debt — showing how each payment splits between interest and principal, and how the running balance falls over time. The schedule is the same arithmetic that drives every fixed-rate installment loan in the U.S. economy. Reading it directly answers most "what if" questions about prepayment, refinancing, and total cost.
The amortization formula and where it comes from
The standard amortization payment is M = P × r(1+r)^n / ((1+r)^n − 1), where P is principal, r is the periodic rate, and n is the number of periods. The formula is derived by setting the present value of n equal payments at rate r equal to the loan amount — solving for the payment that makes the loan exactly pay off at period n.
Each month: interest equals running balance × periodic rate; principal equals the remaining payment after interest; new balance equals old balance minus principal. This monthly recurrence is what an amortization schedule shows; the closed-form payment formula is just the one number that makes the schedule terminate at exactly $0 after n payments.
Reading the schedule
A typical amortization schedule has columns: payment number, payment date, beginning balance, payment, interest, principal, ending balance. Optional columns include cumulative interest, cumulative principal, and (with extras) extra principal payments and revised payoff date.
The interest column starts large and shrinks over time. The principal column starts small and grows. Their sum equals the constant payment amount. The ending balance falls slowly at first, then accelerates — the curve is exponential, not linear.
Comparing loans via the schedule
Two loans with the same monthly payment can have very different total interest depending on rate and term. A 20-year loan at 6% and a 30-year loan at 7% can produce similar monthly payments but very different total cost — the 30-year typically costs 50–100% more interest over the life of the loan despite the lower payment.
Always compare loans on three dimensions: monthly payment (cash flow), total interest (lifetime cost), and rate (the underlying cost of borrowing). The amortization schedule shows all three explicitly. Lender quotes that emphasize only one dimension are common; the schedule cuts through the marketing to the actual numbers.
Extra payments: where in the schedule they go
An extra principal payment in any month immediately reduces the running balance, which reduces every future month's interest. The schedule from that point forward recomputes — same monthly payment, but fewer months remaining and lower total interest. Most lenders apply extra payments to principal automatically when so designated; some apply ahead to next month's payment unless you specify otherwise. Verify with your servicer.
Where in the schedule you make extras matters. An extra payment in month 1 of a 30-year loan eliminates many years of compounded interest; the same payment in month 360 saves nothing because there's only one payment left. The leverage of extra payments is highest at the beginning and tapers steadily over time.
Formula
- M = Periodic payment (constant for fixed-rate loans)
- P = Original principal
- r = Periodic rate (annual rate / periods per year)
- n = Total number of payments
Worked examples
$50,000 auto loan, 6%, 5 years
Monthly payment ≈ $967. Month 1: interest $250, principal $717, new balance $49,283. Month 30: interest ~$135, principal $832, balance ~$26,800. Month 60: interest ~$5, principal $962, balance $0. Total interest paid: $7,995.
Same loan with $200/month extra
Monthly payment $1,167 (regular $967 + extra $200). Loan paid off in ~46 months instead of 60 (saves 14 months). Total interest: ~$5,950 — savings of $2,045.
Comparing 15-year vs. 30-year mortgage on $300,000
30-year at 7%: $1,996/month, total interest $418,500. 15-year at 6.5%: $2,613/month (about $617 more), total interest $170,343. The 15-year costs $617/month more but saves $248,157 in total interest — about 41% of the original loan amount.
Frequently asked questions
Why is the early-month payment mostly interest?
Because interest is calculated on the running balance. In month 1, that balance is the entire principal, so interest is at its maximum. Only the small remainder of the fixed payment goes to principal. As the balance falls month by month, less goes to interest and more retires the loan. This is mathematically inherent to amortization, not a fee or markup.
How is the monthly payment calculated?
The formula M = P × r(1+r)^n / ((1+r)^n − 1) computes the unique payment that makes the loan exactly pay off in n periods at rate r per period on principal P. For a $200,000, 30-year, 7% mortgage: monthly rate 0.5833%, 360 payments. Payment ≈ $1,331/month — the value that, paid for exactly 360 months, retires the loan.
Why does my schedule show a tiny last payment?
Rounding. The standard payment is rounded to cents, so the last payment is adjusted slightly to bring the balance to exactly zero. Some loans round payments differently (always round up, etc.); the result is the same loan, just with a few cents' difference in the final payment.
Can I see the impact of extra payments?
Yes — most amortization calculators support recurring or one-time extra principal inputs. The schedule recomputes from each extra-payment month, showing earlier payoff and lower total interest. The earlier in the loan, the larger the leverage of any extra principal.
Is amortization the same as a balloon payment?
No — fully amortizing loans pay down to zero by the final scheduled payment. Balloon loans amortize at a longer schedule but require the remaining balance in a single large payment at a specified earlier date. Common in commercial real estate; less common (and more dangerous) in residential lending.
What's negative amortization?
When the monthly payment is less than the interest accruing — so the balance grows month by month rather than shrinking. Most adjustable-rate and option-payment loans of the 2000s allowed this, often by design. Modern conventional and government-backed mortgages don't permit negative amortization. It's a structurally dangerous feature for the borrower because the loan grows during the early years.
Related calculators
Concepts
Sources & methodology
- Consumer Financial Protection Bureau — Amortization explained — source