Interest Rate Calculator
Loans & MortgagesSolve for rate, payment or term.
Loan details
Enter a loan amount.
Enter a monthly payment.
Advanced options
Variable-rate scenario
Can't solve with these numbers
That payment is too low to ever repay this loan, so no positive rate fits. Raise the payment or lower the loan amount.
Formulas
| Metric | Formula | Your value |
|---|---|---|
| Implied interest rate | Solved by iteration (no closed form) | 0.00% |
| Monthly payment | P × i ÷ (1 − (1 + i)⁻ⁿ) | $0 |
| Loan amount | M × (1 − (1 + i)⁻ⁿ) ÷ i | $0 |
| Time to pay off | −ln(1 − P·i ÷ M) ÷ ln(1 + i) | 1 mo |
| Total interest | Total repaid − loan amount | $0 |
| Effective annual rate | (1 + i)¹² − 1 | 0.00% |
| APR | Rate that discounts payments to loan − fees | 0.00% |
Your inputs
| Input | What it is | Your value |
|---|---|---|
| Loan amount | The principal you're borrowing | $0 |
| Monthly payment | What you pay each month | $0 |
| Loan term | How long you'll repay over | 0 yrs |
Know what this estimate is based on
- Jurisdiction
- General model; U.S.-specific rules are identified on the relevant tool
- Scope and limitations
- Educational estimate only. A lender may use different compounding, day-count, eligibility, tax, insurance, escrow, fee, or rounding rules.
- Source links checked
- Jul 30, 2026
Built and regression-tested by Smart Tools Lab. It has not been individually reviewed by a licensed financial, tax, or legal professional.
How to use
- 01
Choose what to solve for — interest rate, monthly payment, loan amount or term — with the selector. The other three become your inputs.
- 02
Enter the three known values. To reverse-engineer a rate, give the loan amount, the monthly payment and the term.
- 03
Read the implied rate alongside its APR and EAR, the total interest and repayment, then explore the rate-sensitivity table, fixed-vs-variable comparison and the full amortization schedule below.
Formula
Every fixed-rate loan ties four numbers together with one equation — the amortizing-payment formula: Payment = P × i ÷ (1 − (1 + i)⁻ⁿ) where P is the loan amount, i is the periodic (monthly) interest rate, and n is the number of payments. Knowing any three, the fourth is fixed: • Payment: M = P × i ÷ (1 − (1 + i)⁻ⁿ) • Loan amount: P = M × (1 − (1 + i)⁻ⁿ) ÷ i • Term: n = −ln(1 − P·i ÷ M) ÷ ln(1 + i) • Rate: no closed form — the calculator iterates i until the payment matches (bisection) From the solved figures it derives the rest. Total interest = total of payments − principal. The nominal annual rate is i × 12; the effective annual rate (EAR) compounds it: (1 + i)¹² − 1. If you add an origination fee, the APR is the rate that discounts the payment stream back to the net amount you actually receive (loan − fee), so APR ≥ the nominal rate.
Example
Borrow 250,000, pay 1,580 a month, repay over 30 years (360 payments). Iterating the loan equation lands on a nominal rate of about 6.5%. Over the full term you repay roughly 568,800 — of which about 318,800 is interest, so interest is about 56% of everything you repay. Compounded monthly, that 6.5% nominal rate is an effective annual rate (EAR) of about 6.70%. Add a 2% origination fee (5,000) and the true cost rises to about 6.69% APR. Paying an extra 200 a month would save roughly 97,600 in interest and clear the loan about 8 years early.
Definitions
- Nominal rate
- The quoted annual interest rate, before compounding or fees — equal to the monthly rate × 12.
- APR
- Annual percentage rate: the nominal rate adjusted for the origination fee, so it reflects the loan's true yearly cost. Equal to the nominal rate when there is no fee.
- EAR
- Effective annual rate: the nominal rate compounded monthly, (1 + i)¹² − 1. Always a touch above the nominal rate.
- Principal
- The loan amount you borrow and must repay, separate from the interest charged on it.
- Term
- How long you repay over, here in years. A longer term lowers the payment but raises total interest.
- Amortization
- The way each payment splits between interest and principal, with the principal share growing as the balance falls.
- Total interest
- Everything you pay above the principal: the total of all payments minus the loan amount.
- Origination fee
- A one-off charge to set up the loan, as a percentage of the amount borrowed; it lifts the APR above the nominal rate.
Good to know
What the interest rate really controls
The interest rate is the price of borrowing money, expressed as a percentage of the outstanding balance charged each year. It sounds like a single small number, but it quietly governs almost everything about a loan: how large each payment is, how much you ultimately repay, how long it takes to clear the balance, and how much of every payment is genuinely reducing what you owe versus simply renting the money. A difference of a single percentage point, which looks trivial on paper, can add or remove tens of thousands over the life of a long loan. That is why the rate deserves to be understood on its own terms rather than accepted as a given. This calculator treats the rate as the centre of gravity. Most loan tools assume you already know the rate and project the payment from it; here you can run the logic in any direction — supply a payment and recover the implied rate, or fix the rate and read off the payment, the borrowable amount, or the term. Seeing the rate from every angle is the fastest way to judge whether a quoted deal is fair, what an advertised monthly figure is really charging you, and how sensitive your costs are to the number at the top of the offer.
The one equation behind every loan
Behind every fixed-rate, fully-amortizing loan sits a single relationship that links four quantities: the principal you borrow, the periodic interest rate, the number of payments, and the payment itself. The amortizing-payment formula, Payment = P × i ÷ (1 − (1 + i)⁻ⁿ), is just the arithmetic of paying off a balance in equal instalments while interest accrues on whatever remains. The crucial insight is that this is one equation in four unknowns, so fixing any three pins down the fourth exactly. That is what the solve-for selector does. Give it the loan amount, payment and term and it returns the rate; give it the loan amount, rate and term and it returns the payment; and so on. There is nothing approximate about three of these directions — payment, principal and term each have a clean closed-form rearrangement. Only the rate is special, because it cannot be isolated algebraically. Understanding that one equation underpins all four answers demystifies the whole exercise: you are not running four different calculators, but reading the same fundamental loan relationship from whichever side you happen to know.
Why solving for the rate takes iteration
Three of the four loan variables can be solved with a formula, but the interest rate cannot — it is tangled inside both a division and an exponent, with no way to peel it out algebraically. Instead the calculator solves it numerically, and the method relies on a helpful property: for a fixed loan amount and term, the required payment rises smoothly and steadily as the rate rises. That monotonic behaviour means the answer can be bracketed. The tool starts with a wide range of possible rates, tests the midpoint, and asks whether the resulting payment is too high or too low; it then keeps the half of the range that must contain the true rate and repeats. Each step halves the uncertainty, so after a few dozen iterations the rate that reproduces your exact payment is found to a precision far finer than any lender quotes. This is the same bisection idea used to solve for yields and internal rates of return throughout finance. The practical takeaway is that an implied rate recovered from a payment is every bit as exact as one you type in — the iteration simply does the algebra that the formula cannot.
Nominal rate, APR and EAR — three honest numbers
A loan's cost can be stated in more than one way, and the differences matter. The nominal rate is the headline figure: the annual rate before any compounding effect or fees, equal to the monthly rate multiplied by twelve. The effective annual rate (EAR) takes compounding into account — because interest is charged monthly, a 6% nominal rate actually costs slightly more than 6% over a year, since each month's interest is itself subject to interest. EAR captures that, sitting just above the nominal rate. The annual percentage rate (APR) answers a different question: it folds in upfront costs such as an origination fee. Because a fee means you receive less than the face amount but still repay the full schedule, your true cost is higher, and APR is the rate that reflects it. With no fee, APR equals the nominal rate; with a fee, it exceeds it. The tool shows all three side by side rather than ranking them, because only one ordering is guaranteed — nominal is at or below APR — while EAR can fall on either side of APR depending on the fee. Comparing offers fairly means comparing like with like: APR against APR when fees differ, nominal against nominal when they do not.
How much of your payment is really interest
It surprises many borrowers that, on a long loan, more than half of everything they pay can be interest rather than principal. This is a direct consequence of how amortization works. Interest is charged on the balance still outstanding, and at the start the balance is almost the entire loan, so the early payments are mostly interest with only a sliver reducing the debt. As the balance falls the interest portion shrinks and the principal portion grows, but it takes years for the crossover to arrive. The longer the term, the more pronounced this is. That is why the calculator highlights interest as a share of total payments rather than interest as a multiple of principal. The latter routinely exceeds 100% on a thirty-year loan and reads as alarming even when the rate is perfectly ordinary; the former stays between zero and one hundred percent and genuinely distinguishes a cheap loan from an expensive one. Watching that share is the clearest single signal of how hard your rate and term are working against you, and it is the number that a shorter term or a lower rate moves the most.
Reading the rate-sensitivity table
Rates are rarely fixed in stone when you are shopping — you are weighing offers that differ by a quarter or a half point, or guessing where rates might land before you lock. The sensitivity table is built for exactly that. It holds your loan amount and term constant and steps the rate from two points below your figure to two points above, showing the monthly payment and the total interest at each step. Laid out together, the rows make the cost of rate movements concrete: you can see at a glance what an extra half point adds to the payment, and how much more interest it piles up over the whole term. This turns an abstract worry into a number you can act on. If a lender offers to buy your rate down by paying points, the table shows what that reduction is worth over time, so you can judge whether the upfront cost pays for itself. And if you are simply comparing two quotes, it isolates the effect of the rate alone, with everything else held equal — the cleanest possible apples-to-apples view.
Comparing loan offers without being misled
Lenders compete on the numbers that look best, which are not always the numbers that matter. A low advertised monthly payment can hide a long term that quietly multiplies the total interest; a tempting headline rate can come wrapped in points and fees that lift the true cost well above it. The way to cut through the noise is to compare offers on a like-for-like basis, and this calculator gives you the levers to do it. When two quotes carry different fees, compare their APRs rather than their nominal rates, because APR is the figure that bakes the upfront cost into the yearly rate. When the terms differ, look past the monthly payment to the total interest and the share of payments that interest represents, since a smaller payment stretched over more years often costs more in the end. Use the solve-for selector to normalise an offer to whatever you care about — recover the rate implied by an advertised payment, or fix the rate and term to see what the payment should really be — and use the sensitivity table to value a rate buydown against the points it costs. The discipline is simple: change one variable at a time, hold the rest equal, and judge each offer by total cost over the life of the loan rather than the figure the advertisement leads with.
Fixed versus variable: who carries the risk
A fixed-rate loan charges one rate for the entire term; an adjustable-rate loan (ARM) starts with a lower introductory rate for a few years, then resets to a market-linked rate that can be higher. The choice is really about who carries the risk of future rate moves. A fixed rate hands that risk to the lender, and you pay a small premium for the certainty. An ARM hands the risk back to you in exchange for cheaper payments during the intro period. The comparison in this tool is deliberately two-sided: it computes the lower intro payment, the higher payment after the reset, and the total interest each path produces, then names the cheaper one over the full life of the loan. A generous teaser over a long intro window can genuinely win; a thin discount followed by a steep reset can just as easily lose. The honest way to use it is to look past the attractive early payment and ask whether you could comfortably afford the post-reset payment if rates rose, and whether you expect to sell or refinance before the reset arrives. The intro saving is the reward; the reset payment is the risk you are accepting to earn it.
The outsized power of extra payments
Because interest is charged on the outstanding balance, any money you pay above the scheduled amount goes straight to principal and stops accruing interest for every remaining month of the loan. That makes extra payments unusually powerful, especially early on when the balance — and therefore the interest being charged — is at its highest. A modest extra amount each month can shave years off a long loan and save a large multiple of itself in interest, because each early dollar of principal avoided would otherwise have been charged interest dozens or hundreds of times over. The advanced options let you add an extra monthly amount and the tool reports two things: the interest you save and the time you cut from the term, both measured against the same loan with no extra payments. The effect is non-linear, so it is worth experimenting — doubling the extra payment does not simply double the saving, and the benefit is largest when you start early. For anyone deciding between a shorter term and a longer term with voluntary overpayments, this is the place to see what the overpayments would actually buy.
Amortization: how a loan unwinds
The amortization schedule is the loan's full story told year by year: how much principal and interest you pay in each period, and the balance that remains at the end of it. The chart shows the same thing visually — the balance falling from the full principal towards zero, the cumulative principal paid rising to meet it, and the cumulative interest tracking the growing cost alongside. Read together they make the shape of a loan obvious. The balance line is steep at the end and shallow at the start, the mirror image of the interest-heavy early payments; the gap between principal paid and interest paid narrows and then crosses as the loan matures. Seeing this laid out is more instructive than any single summary figure, because it shows precisely when the loan turns the corner from mostly-interest to mostly-principal. It also makes the effect of the rate vivid: a higher rate tilts the whole schedule towards interest and pushes the crossover later, while extra payments pull it earlier. The schedule is where the headline numbers stop being abstractions and become a month-by-month plan.
Using the tool well, and what it leaves out
This calculator is a precise model of one thing — the loan itself, comprising principal, interest, term and an optional origination fee — and it is most useful when you respect that boundary. It does not include property taxes, homeowners or mortgage insurance, PMI, escrow, late fees, or closing costs beyond the single origination fee, so the payment it shows is the loan payment, not the all-in monthly outgoing on a mortgage. For that fuller picture, the dedicated mortgage, PMI and APR calculators pick up where this one leaves off. It also assumes a fixed rate and equal payments for whichever path you are not explicitly modelling as variable, and it treats the inputs you give as exact. The right way to use it is to isolate the question you actually have: to sanity-check an advertised payment against the rate it implies, to compare offers that differ only by rate, to size what a payment can borrow, or to test how extra payments and shorter terms change the cost. Treat the outputs as a clear, honest model of the loan mechanics — then layer the taxes, insurance and other real-world costs on top before making a final decision.
Frequently asked questions
How does it find the interest rate from a payment?
There is no algebraic formula for the rate, so the calculator solves it numerically. Because the payment rises smoothly as the rate rises, it can bracket the answer and bisect — repeatedly halving the range until the rate that reproduces your exact payment, loan amount and term is found, usually to within a tiny fraction of a percent.
What's the difference between the nominal rate, APR and EAR?
The nominal rate is the quoted rate. APR folds in the origination fee, so it shows the true annual cost of the loan — it equals the nominal rate when there is no fee and is higher when there is one. EAR (effective annual rate) instead reflects monthly compounding, (1 + i)¹² − 1, and sits slightly above the nominal rate. They answer different questions, so the tool shows all three rather than assuming one ranking.
Why does total interest come out larger than the loan amount?
On a long loan it usually does. Interest is charged on the outstanding balance every month, and early on the balance is almost the full principal, so most of each payment is interest. Over 30 years those charges accumulate, often exceeding the original amount. That is why the tool reports interest's share of total payments — a far more telling figure than interest versus principal, which any long loan pushes past 100%.
Can I solve for the loan amount or the term instead of the rate?
Yes. The selector lets you solve for any of the four variables. Solve for payment to see what a loan will cost each month, for loan amount to find how much a given payment will support, or for term to see how long a payment takes to clear a balance. The other three fields are always your inputs.
How do extra payments change the result?
An extra amount paid every month goes straight to principal, shrinking the balance faster than scheduled. That cuts the interest charged in every later month and clears the loan early. The advanced options let you add an extra payment and the tool shows the interest saved and the time shaved off, compared with sticking to the scheduled payment.
What does the rate-sensitivity table show?
It holds your loan amount and term fixed and steps the rate from two points below to two points above your figure, showing the monthly payment and total interest at each. It is the quickest way to see how much a quarter- or half-point really matters, and to compare offers that differ only by rate.
How does the fixed-vs-variable comparison work?
It pits your fixed rate against an adjustable-rate loan (ARM) that starts at a lower intro rate for a set number of years, then resets to a higher rate. The tool computes the lower intro payment, the higher payment after the reset, and the total interest each way, then tells you which is cheaper over the life of the loan — a genuinely two-sided comparison, since a good teaser can win and a steep reset can lose.
Does this include taxes, insurance or PMI?
No. It models the loan itself — principal, interest, term and an optional origination fee. Property taxes, homeowners or mortgage insurance, and other escrow costs are not included. Use the dedicated mortgage, PMI or APR calculators when you need the all-in monthly figure.