Calculator overview
Inputs and outputs
This summary comes from the calculator's published input and output contract.
Inputs
- Principal (required)
-
Unit $ Default 20000 Range At least 0
About this input
How much is borrowed, before any fee the lender adds. Everything else follows from it: the payment, the interest and every row of the schedule scale with this figure, so a fee rolled into the loan belongs here rather than being left out. There is no ceiling on it, because an amount of money has no natural one.
- Term Years (required)
-
Unit years Default 5 Range 1 to 40
About this input
How long the loan runs, in years. It decides the payment more strongly than anything except the amount borrowed, and it is the input most worth moving: a longer term buys a smaller payment and costs more interest, every time. The top of the range is forty years because a forty year loan exists, not because one is ordinary; past thirty years the status line says so.
- APR (required)
-
Unit fraction Default 0.07 Range 0 to 0.25
About this input
The annual percentage rate on the loan. It is divided by twelve to get the rate charged each month, which is the convention a stated APR implies. A lender who charges on a daily balance will differ from this by the timing of payments inside the month. Enter it as a percentage, so seven percent is 7.0%. Zero is allowed and answered: a nought percent loan is a plain division of the amount by the number of months.
- Extra Monthly Payment
-
When omitted Blank
Unit $/month Default Not set Range 0 to 5000
About this input
Optional. An amount paid every month on top of the scheduled payment, which goes entirely to the balance. Leave it blank if there is none, and the two paths reported below are then the same path. It is deliberately kept out of the yearly schedule, which stays the schedule the loan was written on, so that what the extra saves can be read as a difference rather than hidden inside the rows. An early repayment charge, where one applies, can take back much of that saving and is not modelled.
Outputs
- Table1 Payment Row Axis
-
No unit declared
About this output
The values down the left of the payment table: the annual percentage rate, in steps of one point either side of yours and never below zero. Read a row to hold the rate fixed and vary the term. The middle entry is your own rate.
- Table1 Payment Row Input
-
Unit fraction
About this output
Machinery, and NOT an input. Excel substitutes each value from the row axis into this cell while it fills the table; the rest of the time it mirrors APR. Change APR above, never this: the axis is derived from it, so editing the mirror moves the axis while the table walks and the table comes out meaningless.
- Table1 Payment Column Input
-
Unit years
About this output
Machinery, and NOT an input. The same for the column axis: Excel substitutes into it while filling the table, and the rest of the time it mirrors Term_Years.
- Table1 Payment Corner
-
Unit currency/month
About this output
Machinery. Excel requires the formula being tabulated to sit in the payment table's top-left corner, where it means nothing to a reader, so it is formatted away. It holds Monthly_Payment.
- Total Paid
-
Unit $
About this output
The amount borrowed and the interest together, which is what the loan takes out of your income over its life. Compare it with the amount borrowed rather than with the payment: the ratio between the two is the honest price of the term you chose.
- Yearly Schedule
-
No unit declared
About this output
One row for each year the loan runs: the year, how much of that year's payments went to the balance, how much went to interest, and what was still owed at the end of it. Years the loan does not reach are blank rather than zero, because a zero would read as a year in which nothing was paid. The extra payment is deliberately absent from these rows, which show the loan as it was written.
- Table1 Payment Values
-
Unit currency/month
About this output
The body of the payment table: the monthly payment on the same amount borrowed, worked out again for every combination of the two axes. One hundred and twenty-one cells, each one the whole calculation run again. It is a component of the table rather than a result on its own.
- Total Interest
-
Unit $
About this output
Everything the loan charges in interest, added up over every month it runs. This is the figure a payment box hides: two loans with the same monthly payment can differ by years of interest, and the only thing that decides it is how long the balance is outstanding.
- Interest Saved By Extra
-
Unit $
About this output
How much interest the extra payment avoids over the life of the loan. Money sent to the balance stops accruing at the loan's own rate, so this is what that rate earns on it; where an early repayment charge applies, part of this saving goes back to the lender and that charge is not modelled here.
- Model Status
-
No unit declared
About this output
Reads OK, or explains why the inputs are not valid or why the answer deserves a second look.
- Crossover Year
-
Unit years
About this output
The first year in which more of what you paid went to the balance than to interest. On a short loan it is the first year. On a thirty year loan at six and a half percent it is the twentieth, which means nineteen years in which the larger part of every payment bought nothing. Zero means it never happens within the term, which is what a very long term at a high rate produces.
- First Year Interest Share
-
Unit fraction
About this output
How much of the first year's payments went to interest rather than to the balance. It is the clearest single measure of how front loaded a loan is: a short cheap loan sits near a quarter, a long expensive one near nine tenths. It is the same quantity the crossover year reports as a date rather than a proportion.
- Months With Extra
-
Unit months
About this output
How many payments the loan takes once the extra is added to every one of them. With no extra entered it equals the months above, because the two paths are then the same path. The difference between the two is what the extra buys in time, and the figure below is what it buys in money.
- Table1 Payment Column Axis
-
No unit declared
About this output
The values across the top of the payment table: the term in years, in steps of two years either side of yours and never shorter than a year. Read a column to hold the term fixed and vary the rate. The middle entry is your own term, and a short term makes the floor repeat near the left of this axis, which is the table running out of room rather than an error.
- Monthly Payment
-
Unit $/month
About this output
The level payment that clears the balance over the term. It is the same every month, which is what amortising means, and only the split between interest and principal moves. It carries no tax, no insurance and no fee, so a lender's quote will be higher wherever it includes any of those.
- Months
-
Unit months
About this output
How many monthly payments the scheduled payment takes. On a loan that runs to its term this is the term in months; it is reported because the schedule is unrolled rather than assumed, and a term longer than the model unrolls would show up here rather than being quietly cut short.
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Methodology
Purpose and model boundary
Use this to work out the monthly payment on a plain amortising loan and to read the schedule that payment produces, year by year: how much of each year went to the balance, how much went to interest, and what was still owed at the end of it. It also reports how much of the first year's payments is interest, the year in which principal finally overtakes interest, and what an optional extra monthly payment is worth beside the schedule as written.
It prices a level instalment loan with one rate and one term. It carries no tax, no insurance and no fee, so a lender's quote will be higher wherever it includes any of those.
Inputs and units
| Input | Unit | Accepted range | What it means |
|---|---|---|---|
| Principal | $ | 0 or more | How much is borrowed, before any fee the lender adds. Everything else follows from it: the payment, the interest and every row of the schedule scale with this figure, so a fee rolled into the loan belongs here rather than being left out. |
| APR | % | 0% through 25% | The annual percentage rate on the loan. It is divided by twelve to get the rate charged each month, which is the convention a stated annual rate implies. A lender who charges on a daily balance will differ from this by the timing of payments inside the month. A rate of nothing is allowed and answered: it makes the loan a plain division of the amount by the number of months. |
| Term Years | years | 1 through 40 | How long the loan runs. It decides the payment more strongly than anything except the amount borrowed, and it is the input most worth moving: a longer term buys a smaller payment and costs more interest, every time. The top of the range is forty years because such a loan exists, not because one is ordinary. |
| Extra Monthly Payment | $/month | 0 through 5,000 | Optional. An amount paid every month on top of the scheduled payment, which goes entirely to the balance. It is deliberately kept out of the yearly schedule, which stays the schedule the loan was written on, so that what the extra saves can be read as a difference rather than hidden inside the rows. |
Governing relationships
The monthly rate is the annual rate divided by twelve, and the number of payments is the term in years times twelve.
The payment is the level amount that clears the balance over that many payments at that monthly rate, which is the standard annuity payment: the amount borrowed times the monthly rate, divided by one less the monthly rate plus one raised to minus the number of payments. At a rate of nothing the formula collapses to the amount borrowed divided by the number of payments.
Each month is then charged one month of interest on the balance standing at the start of it, the payment is applied, and whatever is left of the payment reduces the balance. That split is what moves across the life of the loan: early on, most of the payment is interest, because the balance it is charged on is largest.
The crossover year is the first year in which more of what you paid went to the balance than to interest. The share of the first year's payments that is interest is the same quantity stated as a proportion rather than as a date.
Calculation sequence
This is the order in which the reported figures depend on one another, each step traceable to what the calculator says a figure is built from. It is not a claim about the order in which the workbook evaluates its own cells.
- Turn the annual rate into a monthly one and the term into a number of payments.
- Work out the level payment that clears the amount borrowed over those payments.
- Unroll the schedule month by month, splitting each payment into interest and principal and carrying the balance forward.
- Sum each year's months into a row: the principal paid, the interest paid, and the balance at the end of that year.
- Add every month of interest together to get what the loan charges in all, and add that to the amount borrowed to get what you hand over.
- Read the first year's split as a proportion, and find the first year in which principal exceeds interest.
- Unroll the schedule a second time with the extra added to every payment, to get the months it takes and the interest it avoids.
- Rerun the payment across a grid of rates and terms, so the two figures on an offer letter can be read against each other.
Outputs and interpretation
| Output | Role | Unit | What it means |
|---|---|---|---|
| Monthly Payment | primary | $/month | The level payment that clears the balance over the term. It is the same every month, which is what amortising means, and only the split between interest and principal moves. It carries no tax, no insurance and no fee. |
| Total Interest | primary | $ | Everything the loan charges in interest, added up over every month it runs. This is the figure a payment box hides: two loans with the same monthly payment can differ by years of interest, and the only thing that decides it is how long the balance is outstanding. |
| Crossover Year | primary | years | The first year in which more of what you paid went to the balance than to interest. On a short loan it is the first year. On a long loan at a high rate it can be most of the way through, which means years in which the larger part of every payment bought nothing. Nothing here means it never happens within the term. |
| Months | detail | months | How many monthly payments the scheduled payment takes. On a loan that runs to its term this is the term in months; it is reported because the schedule is unrolled rather than assumed. |
| Total Paid | detail | $ | The amount borrowed and the interest together, which is what the loan takes out of your income over its life. Compare it with the amount borrowed rather than with the payment: the ratio between the two is the honest price of the term you chose. |
| First Year Interest Share | detail | % | How much of the first year's payments went to interest rather than to the balance. It is the clearest single measure of how front loaded a loan is, and it is the same quantity the crossover year reports as a date rather than a proportion. |
| Months With Extra | detail | months | How many payments the loan takes once the extra is added to every one of them. With no extra entered it equals the months above, because the two paths are then the same path. |
| Interest Saved By Extra | detail | $ | How much interest the extra payment avoids over the life of the loan. Money sent to the balance stops accruing at the loan's own rate, so this is what that rate earns on it. Where an early repayment charge applies, part of this saving goes back to the lender and that charge is not modelled here. |
| Yearly Schedule | detail | One row for each year the loan runs: the year, how much of that year's payments went to the balance, how much went to interest, and what was still owed at the end of it. Years the loan does not reach are left blank rather than shown as nothing, because a zero would read as a year in which nothing was paid. The extra payment is deliberately absent from these rows, which show the loan as it was written. |
Model Status reads OK, or explains why the inputs are not valid or why the answer deserves a second look. It is shown alongside the results rather than in place of them.
The calculator also returns a grid that reruns the payment across a range of rates and terms at once. Its axes, corner and body arrive as separate values and are the grid's parts rather than results to read on their own; the page assembles them into the table.
Every figure above is returned by the model. The page arranges and formats them; it computes none of them.
Validation and status logic
These are the states the delivery's own recorded runs exercise, so the table records what this calculator has been observed to return rather than every branch it could take. A figure that moves with the inputs is shown as ….
| Condition | Returned status |
|---|---|
| No term has been entered | NOT VALID: enter a term of at least one year; a loan with no term has no schedule to draw |
| Nothing has been borrowed | CHECK: nothing has been borrowed, so every figure below is zero |
| The term is longer than an ordinary consumer loan runs | CHECK: a term of … years is longer than an ordinary consumer loan runs, and over that long the interest is the larger part of what you pay |
| The extra clears the loan inside a single year | CHECK: that extra clears the loan in … months, under a year, so the schedule holds a single row |
| The schedule runs past the months this model unrolls | CHECK: the schedule runs past the 480 months this model unrolls, so the figures cover only that much of it; shorten the term |
| None of the preceding conditions applies | OK |
Assumptions and limitations
- Interest is charged once a month, at the annual rate divided by twelve, with the payment falling at the end of the month. A lender charging on a daily balance will differ by the timing of payments inside the month.
- The rate is fixed for the whole term. An adjustable rate loan is not modelled.
- The payment carries principal and interest only. Property tax, insurance, association dues, mortgage insurance and any lender fee are all outside it, so a real quote including them will be higher.
- A fee the lender adds to the loan belongs in the amount borrowed. A fee paid separately at the start is not modelled at all.
- An early repayment charge, where one applies, can take back much of what the extra payment saves and is not modelled.
- The yearly schedule shows the loan as it was written, without the extra. That is deliberate, so the extra's effect can be read as a difference rather than hunted for inside the rows.
Restrictions and non-computing states
This calculator enforces the numeric limits recorded above before the schedule is unrolled, so a value outside them is refused rather than answered.
A term of at least one year is required, because a loan with no term has no payment and no schedule. An amount borrowed of nothing is answered rather than refused, with every figure reading nothing and the status line saying why.
The schedule is unrolled for a limited number of months. A term longer than that window is followed only as far as the window reaches, and the status line says the figures cover that much of it rather than the whole loan.
Errors and warnings
NOT VALID means the inputs do not describe a loan this calculator can answer, and the figures beside it should not be relied on. CHECK is not an error: the arithmetic is sound and the figures stand, but something about the combination is worth knowing first, such as a term long enough that interest is the larger part of what you pay. The status is shown with the results rather than in place of them, so a flagged answer is still a readable one.
A value the page itself refuses, because it falls outside the limits above, is rejected before the calculation is requested and no figures are returned at all. That is different again from a transport or service failure, where the page reports that the result could not be fetched rather than showing a stale or partial one.
References
The periodic payment formula used here, and the convention of dividing a stated annual rate by twelve to reach a monthly one, are set out in the Wikipedia entry on the amortization calculator.
How a level payment splits between interest and principal, with most of each early payment going to interest and more going to principal as the balance falls, is explained by the Consumer Financial Protection Bureau in How does paying down a mortgage work?
These sources provide background; they do not supply the calculator's assumptions or certify its result. This calculator is informational and is not financial, investment, or tax advice. A lender's quote will differ wherever it includes tax, insurance, fees or a different charging basis, and an early repayment charge is not modelled here.
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