Two questions, one loan
Every repayment problem is one of two shapes, and which one you have decides everything else.
The first is you know how long you want to take. You have decided on five years, or your lender has, and the question is what that costs each month. The second is you know what you can pay. There is a fixed amount left over after the rest of your bills, and the question is when the debt finally goes away. The two tabs on this page solve those separately, from the same underlying formula run in different directions.
Most calculators only do the first. The second is the more useful one when the debt already exists rather than being something you are about to take on, because a payment is a thing you can actually control and a term is usually a consequence rather than a choice.
The formulas, both directions
Everything starts with the interest rate for a single payment period, written here as i, with P the balance, n the number of payments and A the payment itself.
Solving for the payment uses the standard amortizing loan formula. It is the present value of an annuity, rearranged:
Solving for the term is the same equation with n made the subject, which requires logarithms because n sits in the exponent:
That expression has a built-in warning. If the payment is smaller than the interest that accrues in one period, the quantity inside the logarithm turns negative and there is no answer — which is exactly right, because such a loan never gets repaid. This calculator checks for that case and tells you the shortfall instead of printing nonsense.
The result is rarely a whole number of payments, and the fractional part is real: it means the last payment is smaller than the rest. A term of 64.9 payments is sixty-four full ones plus a final part-payment, which is how the schedule below is built.
Compounding is not the same as paying
These two dropdowns get confused constantly, and they do different jobs.
Compounding is how often unpaid interest is added to the balance. It is a property of the loan agreement. Pay back is how often you hand money over. A loan can compound monthly and be paid weekly, or compound daily and be paid annually, and the two never have to match.
When they do differ, the quoted rate has to be converted into a rate for one payment period. With r the yearly rate, c compounding periods a year and p payment periods a year:
Continuous compounding is the limit of that as c grows without bound, which collapses to the exponential:
Two conventions are worth stating because they change the arithmetic slightly. Biweekly means 26 periods a year, from 52 weeks. Daily means 365.25 a year, which averages in leap years rather than pretending they do not exist.
What to put in each field
- Loan balance. What is owed right now, not what was originally borrowed. For a payoff figure, ask the lender: it includes interest accrued since the last payment and is usually a little above the statement balance.
- Interest rate. The yearly rate from the agreement. If the document quotes an APR, leave compounding on monthly, which is the usual United States convention for consumer credit.
- Compounding. Change this only if the agreement says so. Annually is labelled APY because when compounding happens once a year the nominal rate and the effective rate are the same number.
- Pay back. How often you make a payment. Changing this alone is a fair way to test whether a weekly or biweekly arrangement is worth asking your lender for.
- Repay over. Years and months, in the term tab. It is converted into payment periods, so five years of fortnightly payments is 130 of them.
- Each payment. In the payment tab, the amount you will actually pay every period — not the minimum the lender will accept, unless those are the same thing.
Why the early payments barely touch the balance
Interest is charged on what is still outstanding, and at the beginning that is the whole loan. The payment is fixed, so the interest share starts high and the principal share starts low. As principal comes off, the interest charge falls and the principal share grows to fill the space it left. The schedule accelerates toward the end.
On short consumer loans the effect is mild. On long ones it is severe: over thirty years, the point at which half the principal has been repaid arrives closer to year twenty than year fifteen. This is also why an extra payment early is worth far more than the same payment late — it removes every future interest charge that dollar of principal would have attracted, and there are more of those charges at the start.
The chart above the schedule shows this directly. The navy portion of each year is principal, the amber is interest, and the grey line is the balance falling. On a long term the amber portion dominates the early bars and has almost vanished by the end.
Paying it off sooner, and whether you should
The mechanics are simple and the decision is not.
Extra payments are the most direct route. Where there is no prepayment penalty, anything above the scheduled amount reduces principal immediately, and the saving compounds for the rest of the term. Confirm with the lender that extra money is applied to principal rather than held as a prepaid future instalment, which some servicers do by default.
Biweekly payments work mostly because 26 half-payments is thirteen monthly payments rather than twelve. It is a budgeting trick more than a mathematical one, and a good one if you are paid fortnightly, but be aware that some lenders charge to set it up and some third-party services charge more.
Refinancing replaces the loan with a cheaper one. The rate saving is real, the closing costs are paid upfront, and the trap is the term: rolling the balance into a fresh long term can raise total interest even at a lower rate. Compare the total-of-all-payments figure, not the payment.
Whether any of this is wise depends on the rate. Paying off debt at 22% is close to a guaranteed 22% return. Paying off a 4% loan while carrying no emergency fund, or while an employer retirement match sits unclaimed, is a worse use of the same money. Clear the expensive debt first and let the cheap debt run its course.
What this calculator does not model
- Fees. Origination charges, late fees and prepayment penalties are outside the model, and origination fees in particular make the effective cost higher than the rate suggests.
- Variable rates. The rate is treated as fixed for the whole term. An adjustable loan changes payment or term at each reset, and nobody can forecast the index it follows.
- Revolving credit. Credit cards recalculate a minimum payment from the balance each month rather than following a fixed schedule. Model a card here by choosing a flat payment you will genuinely keep making.
- Extra and irregular payments. Every payment is assumed to be the same size and to arrive on time.
- Tax. Interest that is deductible, such as some mortgage and student loan interest in the United States, lowers the real cost in a way not shown here.
- Rounding at the lender. Servicers round to the cent in their own way and may adjust the final payment, so the last line can differ by a few cents from your statement.
Frequently asked questions
How long will it take to pay off my loan?
Switch to the “I know the payment” tab, enter what you owe, the rate and what you can pay each period, and the answer comes back as a term and a payment count. The relationship is not linear, which is the part that surprises people: raising a payment by a quarter usually cuts the term by far more than a quarter, because every extra dollar of principal removes all the future interest that dollar would have carried.
What is the formula for a loan repayment?
The payment on an amortizing loan is P x i / (1 - (1 + i)^-n), where P is the balance, i is the interest rate for one payment period and n is the number of payments. Rearranged to solve for the term instead, it becomes n = -ln(1 - P x i / A) / ln(1 + i), with A as the payment. Both are shown worked through on this page, and the second one is what the payment tab uses.
What is the difference between APR and APY on a loan?
APR is the nominal yearly rate before compounding is applied; APY is what the loan actually costs once compounding is counted, so APY is always the higher figure. A rate of 10% compounded monthly is an APY of 10.47%, and compounded daily it is 10.52%. Most United States consumer loans quote APR, which is why this calculator defaults to monthly compounding, but the effective annual rate is shown alongside so the two are never confused.
Do biweekly payments really pay off a loan faster?
Yes, and mostly for an arithmetic reason rather than a clever one. Paying half the monthly amount every two weeks means 26 half-payments a year, which is thirteen monthly payments rather than twelve, so you are simply paying more each year. There is a second, smaller gain: the balance drops a fortnight sooner each time, so slightly less interest accrues. Check for prepayment penalties first, and confirm the lender applies the extra to principal rather than holding it.
Should I pay off my loan early?
It depends on the rate and on what else the money would do. Clearing high-rate debt such as a credit card is close to a guaranteed return equal to the rate, which is hard to beat elsewhere. A low-rate loan is a different question: an emergency fund, an employer retirement match, or higher-rate debt held at the same time all have a stronger claim on the cash. Check the loan agreement for a prepayment penalty before committing, since some auto and personal loans still carry one.
What happens if I only make the minimum payment?
On an amortizing loan with a fixed schedule the minimum is the scheduled payment, so you simply finish on time. On revolving credit such as a card the minimum is recalculated as a small percentage of the balance, so it shrinks as the balance does and the payoff stretches out for years. Enter the balance, the rate and a fixed amount you will actually keep paying in the payment tab to see how a flat payment compares.
Why does so much of an early payment go to interest?
Because interest is charged on the balance that is still outstanding, and at the start that balance is at its largest. The payment stays the same each period, so as the balance falls the interest slice shrinks and the principal slice grows to fill the gap. The schedule on this page shows the crossover directly, and it arrives later than most people expect on long terms: on a thirty-year loan the halfway point in principal repaid is nearer year twenty than year fifteen.
How does the compounding frequency change what I pay?
Compounding sets how often unpaid interest is added to the balance, so more frequent compounding means slightly more interest even at the same quoted rate. On the reference case of a $10,000 loan at 10% over five years, monthly compounding gives a payment of $212.47 while annual compounding gives $210.36, a difference of about $127 over the whole term. The gap widens with larger balances and longer terms, which is why the compounding basis is worth checking on any loan agreement.
This is an educational estimate, not financial advice. Figures exclude fees, penalties and tax relief, assume a fixed rate and identical on-time payments throughout, and may differ from a lender statement by a few cents because servicers round in their own way. Always work from an official payoff quote and the loan agreement before acting on a repayment plan, and check for a prepayment penalty before paying anything early. More about how we build and check these tools is on our About page, and our Privacy Policy explains what we do and do not collect — nothing you type here leaves your browser.