Sigma Calculator — 543+ Free Calculator Tools
See your monthly payment, total interest and year-by-year amortization schedule for any mortgage amount, rate and term.
Enter the loan amount, annual interest rate and term in years. The calculator applies the standard amortization formula and instantly shows your monthly payment, total interest, total cost and a year-by-year schedule of interest, principal and remaining balance.
Formula: Monthly payment = P × r(1+r)^n ÷ ((1+r)^n − 1), where r = annual rate ÷ 12 and n = years × 12. Example: $300,000 at 6.5% for 30 years → $1,896.20/month, $382,633.47 total interest.
Quick answer: A $300,000 mortgage at 6.5% interest repaid over 30 years costs $1,896.20 per month — 360 payments totaling $682,633.47, of which $382,633.47 is interest. Amortization is the process of paying off a home loan through fixed monthly payments, where each payment is split between interest and principal: early payments are mostly interest, while later payments are mostly principal. Enter your own loan amount, rate, and term in the calculator above for exact figures, then read the full guide below for step-by-step instructions, how mortgage amortization works, the formula with fully worked examples, two detailed home-buying scenarios, the five costliest mistakes, and related tools.
Using the Mortgage Amortization Calculator takes under a minute. You enter the loan amount, the annual interest rate, the loan term in years, and the start date — and it instantly shows your monthly payment, total interest, total cost, and a year-by-year amortization schedule. Here is how to use it well.
Step 1 — Enter the loan amount (principal). Type the amount you are borrowing, which is the home price minus your down payment. Example: for a $375,000 home with a 20% down payment ($75,000), enter $300,000. Borrowing precisely what you need matters because every extra $10,000 borrowed at 6.5% over 30 years adds about $63.21 per month and roughly $12,754 in total interest.
Step 2 — Enter the annual interest rate. Use the rate from your loan estimate, not an advertised "starting at" figure. In 2025–2026, typical 30-year fixed mortgage rates have ranged roughly from 6% to 7.5% depending on credit score, down payment, and market conditions. Example: entering 6.5% versus 7.5% on a $300,000, 30-year loan changes the payment from $1,896.20 to $2,097.65 — a $201.45 monthly difference and $72,521 more interest over the life of the loan.
Step 3 — Choose the loan term in years. The most common terms are 30, 20, and 15 years. Shorter terms mean higher monthly payments but dramatically less total interest. Example: that same $300,000 at 6.5% costs $1,896.20/month over 30 years ($382,633.47 interest) but $2,612.90/month over 15 years ($170,322 interest) — the shorter term saves $212,311 in interest.
Step 4 — Set the start date. Enter the month your first payment is due. The schedule labels each year of the loan from this starting point, so you can see exactly where you will stand at any future date — useful when planning a refinance or a sale.
Step 5 — Read the three headline numbers and the schedule. The calculator shows your monthly payment ($1,896.20 in our example), total interest ($382,633.47), and total cost ($682,633.47). Below that, the year-by-year table shows how much interest and principal you pay each year and your remaining balance — watch the interest column shrink and the principal column grow as the years pass.
Step 6 — Test scenarios before you commit. Run at least three combinations: your target rate, a slightly higher rate in case your locked rate slips, and a shorter term. If the payment at your likely rate exceeds 28–31% of your gross monthly income — the traditional front-end housing ratio lenders use — the home may be stretching your budget. Example: on $7,000 of gross monthly income, a $1,896.20 payment is 27.1% — within the safe zone.
Amortization is the gradual repayment of a debt through regular, fixed payments over a set period. With a fixed-rate mortgage, you make the same payment every month for the entire term — 360 identical payments on a 30-year loan — but the internal split of each payment changes constantly. In the early years, most of each payment goes to interest; in the later years, most goes to principal. The amortization schedule is the table that tracks this split payment by payment (or year by year, as in the calculator above), showing interest paid, principal repaid, and the remaining loan balance.
The principal is the amount you borrowed — $300,000 in our running example. The interest is the lender's charge for the use of its money, calculated each month on the outstanding balance. Because interest is charged on the remaining balance, and the balance is highest at the start, the first payments are interest-heavy by mathematical necessity rather than lender trickery. On the $300,000, 6.5%, 30-year loan, the very first $1,896.20 payment contains $1,625.00 of interest and only $271.20 of principal. By the final year, the situation reverses: the payments are almost entirely principal.
This shifting split is why equity — the portion of the home you truly own, equal to the home's value minus the remaining loan balance — builds slowly at first. After one year of payments on our example loan, you have repaid only $3,353.18 of principal (your down payment counts as day-one equity on top of that). After 10 years and $227,544 in total payments, the balance is still $254,328.38 — you have repaid just $45,671.62 of the $300,000 borrowed. That is the reality amortization reveals: for the first decade, you are mostly paying the lender for the privilege of borrowing.
Understanding this has practical consequences. Extra principal payments made early in the loan destroy far more future interest than the same extra dollars paid near the end, because early extra payments avoid interest accruing over the remaining decades. Selling or refinancing early means most of what you paid went to interest rather than building equity — a key reason financial planners suggest staying in a home at least five to seven years. And when you compare a 15-year with a 30-year mortgage, the 15-year loan's faster principal repayment is exactly why its total interest bill is so much smaller.
The calculator uses the standard amortizing loan payment formula:
M = P × r(1+r)n ÷ ((1+r)n − 1)
Where M is the monthly payment, P is the principal (loan amount), r is the monthly interest rate (annual rate ÷ 12), and n is the total number of monthly payments (years × 12). Total repayment = M × n, and total interest = (M × n) − P.
Worked Example 1. Borrow $300,000 at 6.5% annual interest for 30 years. Step 1: monthly rate r = 0.065 ÷ 12 ≈ 0.00541667. Step 2: number of payments n = 30 × 12 = 360. Step 3: (1.00541667)360 ≈ 6.9918. Step 4: M = 300,000 × 0.00541667 × 6.9918 ÷ (6.9918 − 1) = 11,361.68 ÷ 5.9918 ≈ $1,896.20 per month. Total repayment = 1,896.20 × 360 = $682,633.47; total interest = 682,633.47 − 300,000 = $382,633.47. This matches the calculator above exactly — and notice the sobering result: you repay more in interest ($382,633.47) than you originally borrowed ($300,000).
Worked Example 2. Borrow $250,000 at 7% annual interest for 30 years. Step 1: r = 0.07 ÷ 12 ≈ 0.00583333. Step 2: n = 360. Step 3: (1.00583333)360 ≈ 8.1165. Step 4: M = 250,000 × 0.00583333 × 8.1165 ÷ (8.1165 − 1) = 11,836.60 ÷ 7.1165 ≈ $1,663.25 per month. Total repayment = 1,663.25 × 360 = $598,770; total interest = 598,770 − 250,000 = $348,770. Compare with Example 1: borrowing $50,000 less at a slightly higher rate still costs about $34,000 less in interest — the size of the principal dominates the interest bill.
Quick sanity check you can do mentally: multiply the monthly payment by the number of payments, then subtract the loan amount. If the total interest exceeds the principal — as it does on most 30-year loans above 6% — consider a larger down payment or a shorter term before you sign.
Meet Daniel and Priya, first-time buyers purchasing a $400,000 home. They put 20% down ($80,000) — which also lets them avoid private mortgage insurance — and borrow $320,000 at 6.25% fixed for 30 years. The math: r = 0.0625 ÷ 12 ≈ 0.00520833, n = 360, (1.00520833)360 ≈ 6.4877, so M = 320,000 × 0.00520833 × 6.4877 ÷ 5.4877 ≈ $1,970.37 per month of principal and interest. Total repayment = 1,970.37 × 360 = $709,333; total interest = $389,333.
Their first payment splits into $1,666.67 of interest (320,000 × 0.00520833) and just $303.70 of principal. After five years they will have paid about $118,222 in total, yet their balance will still be roughly $298,660 — only about $21,340 of principal repaid. But their equity position is stronger than those numbers suggest: the $80,000 down payment plus $21,340 of principal repaid gives them over $101,000 of equity before any appreciation, more than 25% of the home's value. If the home appreciates 3% per year, after five years it is worth about $463,710, pushing their equity above $165,000. This is why the down payment matters so much: it is day-one equity that amortization alone builds only slowly.
Their decision rule: with $8,500 of combined gross monthly income, the $1,970.37 payment is 23.2% of income — safely under the 28% front-end ratio most lenders prefer. They also budget escrow separately: roughly $300 per month for property tax and $150 per month for homeowners insurance sit on top of the $1,970.37, making their true monthly housing cost about $2,420. The calculator above shows the principal-and-interest core; always add your local tax and insurance figures for the full picture.
Now meet Robert, 45, refinancing a $300,000 balance at 6.5% and choosing between another 30-year term and a 15-year term. Here are both options, computed with the formula.
Option A — 30 years (360 payments): M ≈ $1,896.20/month, exactly as the calculator above shows. Total repayment = $682,633.47; total interest = $382,633.47.
Option B — 15 years (180 payments): r = 0.00541667, n = 180, (1.00541667)180 ≈ 2.6446, so M = 300,000 × 0.00541667 × 2.6446 ÷ 1.6446 ≈ $2,612.90/month. Total repayment = 2,612.90 × 180 = $470,322; total interest = $170,322.
The trade-off is stark: Option B costs $716.70 more per month but saves $212,311 in total interest and builds equity far faster — after five years the 15-year loan balance is down to about $230,000, versus about $281,000 remaining on the 30-year schedule. Robert's decision rule: the $2,612.90 payment must stay under 28% of gross monthly income ($9,332 for his household) while leaving a six-month emergency fund intact. Because he plans to retire at 62, being mortgage-free at 60 wins — he takes the 15-year term. For a younger buyer who prizes cash-flow flexibility, the 30-year term with voluntary extra principal payments can be the smarter hybrid.
Mistake 1 — Shopping by monthly payment alone. A buyer compares the 30-year payment ($1,896.20) with the 15-year payment ($2,612.90) and reflexively chooses the lower one — paying $212,311 more in interest for the "affordable" payment. Fix: compare total interest first, then verify that the higher payment fits your budget.
Mistake 2 — Ignoring how interest-heavy the early years are. In year 1 of the $300,000 example, $19,401.27 of your $22,754.40 in payments is interest — only $3,353.18 reduces the balance. Borrowers who do not understand this are shocked when, selling after three years, they find their payments built almost no equity. Fix: study the schedule before you buy, and plan to stay at least five to seven years or buy with a larger down payment.
Mistake 3 — Confusing principal and interest with PITI. The amortization schedule covers principal and interest only. Property taxes, homeowners insurance (and PMI if your down payment is under 20%) are collected separately through escrow. A $1,896.20 P&I payment easily becomes $2,400 or more all-in. Fix: budget the full PITI figure — ask your lender for the escrow estimate before you start house-hunting.
Mistake 4 — Never making extra principal payments. An extra $200 per month on the $300,000, 6.5%, 30-year loan pays it off in roughly 23 years instead of 30 and saves about $100,000 in interest. Even making one extra payment per year cuts roughly six years off the loan and saves tens of thousands in interest. Fix: round your payment up or automate a small extra principal amount from day one — early extra dollars are the most powerful because they avoid decades of interest.
Mistake 5 — Refinancing and resetting the amortization clock. Ten years into a 30-year loan you have finally reached the phase where principal repayment accelerates — then you refinance into a brand-new 30-year loan and restart the interest-heavy years. Unless the rate drop is large (typically 0.75–1% or more), the reset can cost more than it saves. Fix: when refinancing, choose a term matching your remaining years (for example, refinance a 30-year loan at year ten into a 20-year loan), and compare lifetime interest — not just the monthly payment.
A mortgage decision rarely stands alone. Use the Mortgage Calculator to estimate payments including taxes and insurance, the Amortization Calculator for a full month-by-month payoff schedule of any loan, and the Loan Calculator to compare other loan structures side by side. Thinking of refinancing later? The Refinance Calculator shows whether a new rate actually saves money after closing costs. Together with the Mortgage Amortization Calculator above, these tools cover every number that matters before you borrow.
Entity: Mortgage Amortization Calculator — computes monthly payment, total interest, total cost, and a year-by-year amortization schedule for a fixed-rate mortgage. Core formula: M = P × r(1+r)n ÷ ((1+r)n − 1); r = annual rate ÷ 12; n = years × 12; total = M × n; interest = total − P. Reference example: $300,000 at 6.5% for 30 years → $1,896.20/month; $682,633.47 total; $382,633.47 interest; 360 payments; year-1 interest $19,401.27, principal $3,353.18; first payment $1,625.00 interest, $271.20 principal. Second example: $250,000 at 7% for 30 years → $1,663.25/month; $598,770 total; $348,770 interest. 15-year comparison: $300,000 at 6.5% for 15 years → $2,612.90/month; $470,322 total; $170,322 interest; saves $212,311 versus 30-year. Key concepts: amortization (fixed payments with shifting interest/principal split), amortization schedule, principal, interest, equity (home value minus remaining balance), escrow and PITI, extra principal payments. Decision rule: housing payment at or below 28% of gross monthly income; compare loans by total interest, not payment alone; extra principal paid early saves the most interest.
Sources: Consumer Financial Protection Bureau — mortgage amortization guidance; Federal Reserve — mortgage rate and household debt data; U.S. Department of Housing and Urban Development — homebuying guidance.
Mortgage amortization is the process of repaying a home loan through fixed monthly payments over a set term. Each payment is split between interest and principal: early payments are mostly interest, while later payments are mostly principal, until the balance reaches zero.
With the amortization formula: payment = principal × monthly rate × (1 + rate)^n ÷ ((1 + rate)^n − 1), where n is the number of payments. For example, $300,000 at 6.5% over 30 years gives $1,896.20 per month. Try the calculator above.
Interest is charged each month on your remaining balance, which is highest at the start. On a $300,000 loan at 6.5%, the first $1,896.20 payment contains $1,625.00 of interest and only $271.20 of principal. As the balance falls, the interest portion shrinks and the principal portion grows.
Make extra principal payments — even $200 extra per month on a $300,000, 6.5%, 30-year loan pays it off in about 23 years instead of 30 and saves roughly $100,000 in interest. Extra payments made early in the loan save the most.
A 15-year term on $300,000 at 6.5% costs $2,612.90 per month with $170,322 total interest, versus $1,896.20 per month and $382,633 in interest over 30 years. The 15-year loan saves $212,311 in interest but requires a $716.70 higher payment.
A table showing how each payment splits between interest and principal and your remaining balance over time. The calculator above generates a year-by-year schedule — for example, in year 1 of a $300,000, 6.5%, 30-year loan you pay $19,401.27 in interest and $3,353.18 in principal.
No. The schedule covers principal and interest only. Property taxes and homeowners insurance are usually collected separately through an escrow account, forming PITI (principal, interest, taxes, insurance) — your true monthly housing cost.
No. It models a fixed-rate mortgage with unchanging payments. With an adjustable-rate mortgage (ARM), the rate — and therefore the payment and schedule — can change after the initial fixed period ends.
Last updated: October 8, 2026