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Loan Amortization Calculator

✦ Finance & Money

Use this free loan amortization calculator to see your exact monthly payment, full amortization schedule with annual rollups, total interest paid, and how extra monthly, lump-sum or annual payments cut your payoff date and interest.

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  • ✓ Formula and sources shown

The formula

Level-payment amortization formula

PMT = P x [r(1+r)^n] / [(1+r)^n - 1]

P = loan amount; r = periodic interest rate (annual rate / periods per year); n = total number of payment periods. Each period: Interest = Balance x r; Principal = PMT - Interest; New Balance = Balance - Principal. The last payment is adjusted to clear the exact remaining balance — rounding never accumulates. Payment rounded to the cent; interest computed on the unrounded balance each period. Source: CFPB, Federal Reserve consumer guide.

Calculating it by hand

  1. Enter the loan amount (the amount borrowed, not the purchase price).
  2. Enter the annual interest rate from your loan documents.
  3. Enter the loan term in years (or months using the toggle).
  4. Choose your payment frequency — monthly is the default; bi-weekly, weekly, quarterly and annual each re-solve the payment for that many periods per year.
  5. Optionally set the first payment date to see calendar payoff dates.
  6. Open "Extra payments" to add a fixed monthly extra, a one-time lump sum, or a recurring annual extra.
  7. Read the monthly payment and total interest in the results panel, then open the schedule to see every period.

Worked examples

$300,000 mortgage at 7% for 30 years (monthly)

  1. r = 0.07 / 12 = 0.005833...
  2. n = 30 x 12 = 360
  3. PMT = 300000 x [0.005833 x (1.005833)^360] / [(1.005833)^360 - 1]
  4. (1.005833)^360 = 8.11650 (full precision)
  5. PMT = 300000 x [0.005833 x 8.11650] / [8.11650 - 1]
  6. PMT = 300000 x 0.047346 / 7.11650
  7. PMT = 300000 x 0.006653 = $1,995.91
  8. Period 1 interest: 300000 x 0.005833 = $1,750.00; principal: $245.91
  9. Payments: 359 x $1,995.91 plus a final payment of $1,992.84 that clears the rounding residual = $718,524.53
  10. Total interest: $718,524.53 - $300,000 = $418,524.53

Monthly payment: $1,995.91 | Total interest: $418,524.53

$25,000 auto loan at 6.5% for 5 years (monthly)

  1. r = 0.065 / 12 = 0.005417
  2. n = 5 x 12 = 60
  3. (1.005417)^60 = 1.38282
  4. PMT = 25000 x [0.005417 x 1.38282] / [1.38282 - 1]
  5. PMT = 25000 x 0.007491 / 0.38282
  6. PMT = 25000 x 0.019568 = $489.15
  7. Period 1 interest: 25000 x 0.005417 = $135.42; principal: $353.73
  8. Payments: 59 x $489.15 plus a final payment of $489.41 = $29,349.26
  9. Total interest: $29,349.26 - $25,000 = $4,349.26

Monthly payment: $489.15 | Total interest: $4,349.26

$300,000 at 7% for 30 years with $200/month extra payment

  1. Base payment: $1,995.91 (same as example 1)
  2. Effective payment: $1,995.91 + $200 = $2,195.91
  3. Run schedule with extra = $200 applied to principal each month
  4. Balance hits zero at month 275 (not 360)
  5. Interest paid with extra: $301,885.68
  6. Interest saved vs no extra: $418,524.53 - $301,885.68 = $116,638.85
  7. Payoff 85 payments (7 years 1 month) earlier than scheduled

Payment: $2,195.91 | Interest saved: $116,638.85 | Term reduced: 85 months

Methodology

How loan amortization actually works

Most borrowers are surprised to discover that their early payments are almost entirely interest. Understanding this front-loading — and why extra payments are most powerful early in the loan — is what turns the schedule from a table of numbers into a tool.

Read sources and limits

Why are my early loan payments mostly interest?

A fully amortizing loan has a fixed payment that never changes, but the split between interest and principal shifts every single period. In period one, interest is calculated on the full loan balance — so on a $300,000 loan at 7%, the first month's interest alone is $1,750. Only the remainder of your payment reduces principal.

As the balance falls, less of each payment goes to interest and more retires principal.

This is why a 30-year mortgage feels like it takes decades to build equity. In the first five years of a $300,000 loan at 7%, you pay $119,754.60 in total payments but reduce your balance by only $17,605.41 — the rest is interest. The schedule makes this visible: look at the "principal paid" column in year 1 versus year 20.

How do extra payments shorten an amortization schedule?

Any amount you pay above the scheduled principal immediately reduces the outstanding balance. Because next month's interest is calculated on that lower balance, a smaller slice of next month's payment goes to interest — and slightly more goes to principal. That compounding effect means every early extra dollar saves more interest than a late extra dollar of the same size.

A one-time $200 extra payment in month 1 of a $300,000, 30-year loan at 7% saves $1,413.88 in total interest — about seven times its size — although on its own it only shrinks the final payment. The same $200 paid in month 300 saves $83.52. Paid every month, $200 extra saves $116,638.85 and 85 payments. Open the extra-payment panel, enter $200 in the monthly extra field, and watch the payoff date and total interest lines update immediately.

Do bi-weekly payments really save money?

Bi-weekly payment plans are often sold as a compounding trick. They are not. The saving comes entirely from making 26 half-payments per year — which equals 13 full payments instead of 12. That one extra payment per year is real: on a $300,000, 30-year loan at 7% it removes 75 payments and saves $102,425.

To model it here, keep the frequency on monthly and enter your payment ÷ 12 ($166.33 in that example) as the monthly extra.

The calculator's Bi-weekly frequency is something different: a loan written with 26 payments a year, its payment re-solved for 780 periods ($920.76 on the same loan, a little less than half the monthly $1,995.91). It makes no 13th payment, so its total interest ($418,204.63) is almost the same as the monthly schedule's.

The catch is servicer behaviour. Many servicers hold each mid-month half-payment in a suspense account until the second half arrives, then post both as one monthly payment on the due date. In that case, your balance does not fall mid-month and you get none of the intra-period interest reduction — only the benefit of one extra annual payment. Always confirm in writing that your servicer credits each half-payment on receipt before relying on the full bi-weekly savings shown.

How does payment frequency change the schedule?

Changing frequency does not change the formula — it changes the periodic rate (annual rate / periods per year) and the total number of periods. Monthly uses 12 periods; bi-weekly uses 26; weekly uses 52; quarterly uses 4; annual uses 1. The payment amount differs because it covers a different share of interest per period.

Weekly payments are not 4x a bi-weekly payment. They are calculated independently as P x [r_w(1+r_w)^N] / [(1+r_w)^N - 1] where r_w = annual rate / 52 and N = term in years x 52. This calculator uses the exact formula for each frequency and does not scale one frequency from another.

Why is the last payment different from the others?

Each payment is rounded to the nearest cent using standard half-up rounding. Interest for each period is then computed on the exact (unrounded) remaining balance, not on a rounded figure. This matches how lenders calculate and means the schedule recreates your actual statement.

The final payment almost always differs slightly from all other payments — it absorbs the accumulated rounding residual and clears the balance to exactly zero.

A $300,000 loan at 7% for 30 years has 359 payments of $1,995.91 and a final payment of $1,992.84 (servicers can differ by a few cents depending on their rounding rules). The "last payment" line in the schedule shows the actual final amount. This calculator always states this convention beside the result, as required by the site's disclosure standard.

Loan Amortization questions

What is an amortization schedule and what does it show?

An amortization schedule lists every payment in a loan — usually monthly — showing how much goes to interest, how much reduces principal, and the remaining balance after each payment. This calculator also adds annual rollup rows so you can see your yearly totals, plus a "with extra payments" column that shows the impact of any additional principal you choose to pay. The full schedule is available to download as a CSV file.

Why is so much of my early mortgage payment interest?

Because interest is always calculated on the remaining balance, and your balance is highest at the start. On a $300,000 loan at 7%, month-one interest is $1,750 — almost 88% of the $1,995.91 payment. As you pay down principal, the interest share shrinks and the principal share grows. This is why extra payments made early have such an outsized effect: they reduce the base on which every future month's interest is calculated.

How do I calculate a loan payment by hand?

Use the formula PMT = P x [r(1+r)^n] / [(1+r)^n - 1], where P is the loan amount, r is the monthly interest rate (annual rate / 12), and n is the number of monthly payments. For a $100,000 loan at 6% for 20 years: r = 0.005, n = 240, (1.005)^240 = 3.310, PMT = 100000 x (0.005 x 3.310)/(3.310 - 1) = 100000 x 0.01655/2.310 = $716.43 per month. Each period's interest is the remaining balance x r; principal = PMT - interest.

Does paying bi-weekly really save money?

Yes — bi-weekly payments create 26 half-payments per year, equivalent to 13 full monthly payments instead of 12. That extra payment per year takes about six years off a 30-year loan at 7% (75 payments and $102,425 of interest on $300,000). This calculator's Bi-weekly frequency is a loan written with 26 smaller payments, not that plan — model the plan with your payment ÷ 12 as a monthly extra. The critical variable is your servicer: some hold mid-month half-payments in a suspense account and only apply them at month-end, eliminating the mid-period interest benefit. Before enrolling in a bi-weekly programme, ask your servicer in writing whether each half-payment is credited on receipt.

What happens if I make an extra payment on my loan?

Any extra amount beyond the scheduled payment reduces your principal immediately. Because next period's interest is calculated on the new lower balance, a slightly larger portion of every subsequent payment goes to principal. The compounding effect means early extra payments save significantly more interest than the same amount paid later. A one-time $5,000 lump sum in month 1 of a $300,000, 30-year mortgage at 7% saves $33,250 in interest and removes 19 payments.

Can I use this for a car loan, student loan or personal loan?

Yes. The level-payment amortization formula is identical for any fully amortizing installment loan — mortgages, auto, personal, student and business term loans all use PMT = P x [r(1+r)^n] / [(1+r)^n - 1]. The main difference is frequency and term. Auto loans are typically 24-84 months; student loans 10-30 years; personal loans 2-7 years. Enter the appropriate rate and term for your loan type and the maths is the same.

Why does my last payment differ from all the others?

Because each payment is rounded to the nearest cent, a tiny rounding residual accumulates across all periods. The final payment absorbs this residual — it is adjusted up or down by a few cents to clear the balance to exactly zero. This is standard lender practice. This calculator always shows the actual last payment amount in the schedule footer and states the rounding convention (payment to the cent; interest computed on the unrounded balance) beside the result.

What is the difference between a fixed-rate and adjustable-rate amortization schedule?

This calculator models a fixed-rate loan: the payment, interest rate and schedule are constant for the full term. An adjustable-rate mortgage (ARM) has a fixed period followed by periodic rate resets, which change both the payment and the schedule at each reset. ARMs cannot be fully scheduled without knowing future rates. For an ARM, use this calculator to model the fixed period and then re-run it at each adjustment with the new rate and remaining balance as a new loan.

Source notes

Method, sources & limitations

Every figure on this page comes from the formula above applied to the values you enter. Nothing is estimated from market data, and no result is a forecast. These are the sources behind the method and any fixed figures it uses:

Educational information only. Results are estimates produced from the assumptions you enter, and are not financial, tax, legal or medical advice. Check anything that matters against a qualified professional and the cited sources.