Payments, interest and principal in each year of the plan, and the balance left at the end of the year. The first row includes any lump sum paid today.
Year
Paid
Interest
Principal
Balance at year end
1
$11,829.92
$4,332.46
$7,497.46
$117,352.07
2
$9,829.92
$4,131.26
$5,698.66
$111,653.41
3
$9,829.92
$3,922.69
$5,907.23
$105,746.18
4
$9,829.92
$3,706.48
$6,123.44
$99,622.74
5
$9,829.92
$3,482.36
$6,347.56
$93,275.18
6
$9,829.92
$3,250.04
$6,579.88
$86,695.30
7
$9,829.92
$3,009.22
$6,820.70
$79,874.60
8
$9,829.92
$2,759.58
$7,070.34
$72,804.27
9
$9,829.92
$2,500.81
$7,329.11
$65,475.16
10
$9,829.92
$2,232.56
$7,597.36
$57,877.80
11
$9,829.92
$1,954.50
$7,875.42
$50,002.38
12
$9,829.92
$1,666.26
$8,163.66
$41,838.72
13
$9,829.92
$1,367.47
$8,462.45
$33,376.27
14
$9,829.92
$1,057.74
$8,772.18
$24,604.09
15
$9,829.92
$736.68
$9,093.24
$15,510.85
16
$9,829.92
$403.87
$9,426.05
$6,084.80
17
$6,163.16
$78.35
$6,084.80
$0.00
Enter today’s balance, the interest rate and what you pay each month. The default is OpenStax’s $140,000 mortgage three years in, with a $2,000 bonus paid off the balance.
Estimates only — not financial, tax, or professional advice.
Calculated in your browser — the numbers you enter are never sent to our servers.
What it calculates: Payments left, Monthly payment needed, Years left, Interest from here on.
A $2,000 prepayment on a $140,000 mortgage saves $1,665.38 of interest and four payments
OpenStax Principles of Finance works a $140,000 mortgage over 20 years at 3.6%: $819.16 a month and $56,597.02 of interest over the life of the loan (Table 8.5). After 36 payments the balance is $124,849.53, which is where this calculator starts by default.
Paying a $2,000 bonus off the balance then leaves 200 payments instead of 204, the last one $429.04 instead of $817.78, and cuts the interest still to come from $42,257.73 to $40,592.35: $1,665.38 saved. Over the whole loan that is $54,931.64 of interest instead of $56,597.02, the “$55,000” OpenStax reports.
OpenStax also describes the loan as ending almost six months early. Worked month by month, it ends four payments early with a half-size final payment, about four and a half months, and the formula below gives 4.48. The interest saving is the part that matches.
OpenStax 8.3, month 36
Balance 124,849.53 at 3.6%, 819.16 a month
Pay 2,000 now: 204 → 200 payments
Interest to come: 42,257.73 → 40,592.35
How many payments are left: n = −ln(1 − r × B ÷ P) ÷ ln(1 + r)
Each month the lender adds interest at the monthly rate r, the APR divided by 12, and the payment P comes off. On the default balance, 3.6% ÷ 12 = 0.3% a month, so the first month’s interest is $374.55 and the other $444.61 of the $819.16 reduces the balance. The formula counts how many such months it takes: 204 without the bonus.
n = −ln(1 − r·B ÷ P) ÷ ln(1 + r)
The formula has a limit built in. If the payment is no more than a month’s interest (r × B), the balance never falls. A $5,000 credit card balance at 24% accrues $100 of interest a month, so a $100 payment never clears it; $110 takes 122 payments and $8,319.96 of interest, and $150 takes 56 payments and $3,322.09.
An extra $100 a month saves $6,507.56 and 29 payments; a one-time $2,000 saves $1,665.38
On the default mortgage, adding $100 to every payment clears it in 175 payments instead of 204 and saves $6,507.56 of interest. The $2,000 lump sum saves $1,665.38. The two are not the same amount of money: the extra $100 a month adds up to far more than $2,000 over the years it runs.
What they share is timing. Every dollar paid early stops carrying interest for the rest of the loan, so a dollar paid in the first year saves more than a dollar paid in the last. That is why a prepayment matters most early in a long loan, when most of each payment is still interest.
FigureA one-time $2,000 barely moves the line but still saves $1,665.38; $100 more every month bends it down and saves $6,507.56.
The payment that clears a loan by a date: P = r × B ÷ (1 − (1 + r)^−n)
Switch “Solve for” to the payment, choose the number of months, and the calculator solves the same schedule for the payment instead. To clear the default $124,849.53 in 10 years (120 months) at 3.6% takes $1,240.44 a month, with $24,003.62 of interest along the way.
P = r·B ÷ (1 − (1 + r)^−n)
The same formula gives a new loan’s payment. OpenStax’s $32,000 car loan at 6% over 36 months comes out at $973.50 a month (the exact figure is $973.502), and its 36 payments carry $3,046.08 of interest, as its Table 8.4 shows. A payment rounded down to the cent leaves 8 cents over at the end; the calculator folds a remainder under $1 into the final payment, as lenders do.
OpenStax 8.3, car loan
32,000 at 0.5% a month for 36 months
P = 160 ÷ (1 − 1.005^−36) = 973.50
Interest over the loan: 3,046.08
Before you prepay: penalties, higher-rate debt, and making sure the money reaches the principal
Some mortgages carry a prepayment penalty. The Consumer Financial Protection Bureau explains that it usually applies when the whole balance is paid off within a set number of years, often three or five, sometimes when a large amount is paid at once, and not normally when small extra amounts go to principal. Check the loan agreement or ask the lender before sending a lump sum.
Tell the lender that extra money is for principal, and check the next statement: an extra payment treated as an early regular payment does not shorten the loan in the same way.
If you hold more than one debt, the highest rate usually deserves the extra money first: a dollar off a 24% card saves far more than a dollar off a 3.6% mortgage. The Debt Payoff Calculator compares paying debts in order of rate or of size.
This page, the Amortization Calculator and the Debt Payoff Calculator each start from a different place
The Amortization Calculator builds a new loan from its original amount and term, with extra payments and the full month-by-month schedule. This page starts from the balance on today’s statement, which is what you know part-way through a loan, and answers the payoff questions directly: how long is left, what an extra payment saves, and what it takes to finish by a date.
The Debt Payoff Calculator takes several debts at once and compares the snowball and avalanche orders. For a single loan you already have, this page is the shorter route.
Frequently Asked Questions
How do I calculate how long it will take to pay off a loan?
With the balance B, the monthly rate r (APR ÷ 12) and the payment P: n = −ln(1 − r·B ÷ P) ÷ ln(1 + r), rounded up to whole payments. The calculator runs the schedule month by month and gives the final payment too.
How much interest will I save by paying extra?
Enter the extra amount and the calculator compares the schedule with and without it. On the default $124,849.53 mortgage balance at 3.6%, an extra $100 a month saves $6,507.56 and 29 payments.
What payment do I need to pay off a loan in a set time?
P = r·B ÷ (1 − (1 + r)^−n) for n months. Clearing $124,849.53 at 3.6% in 10 years takes $1,240.44 a month.
Why does the calculator say my loan will never be paid off?
Because the payment does not cover a month’s interest: at 24%, a $5,000 balance accrues $100 a month, so a $100 payment leaves the balance where it was. Any payment above the monthly interest eventually clears it.
Is a lump sum or extra monthly payments better?
Both cut interest, and earlier money saves more than later money, because it stops carrying interest sooner. Compare them in the calculator with the amounts you can actually afford.
Is there a penalty for paying off a loan early?
Some loans have one. The CFPB notes that mortgage prepayment penalties usually apply to paying off the whole balance within a few years, not to small extra principal payments. Check your loan agreement.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.
Results are estimates based on the figures you enter and standard formulas. Rates, fees, taxes, and lender terms vary and change over time, so confirm important numbers with your lender or a qualified professional. This is educational information, not financial advice.
Published the loan payoff calculator: from today’s balance, the payments left, the final payment, the interest and payments an extra monthly amount or a lump sum saves, and the payment that clears the loan by a chosen date.
Checked against OpenStax Principles of Finance 8.3 (Tables 8.4 and 8.5, and the $2,000 prepayment), where the schedule shows the prepaid mortgage ending about four and a half months early rather than the six the text gives.
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