Loan Balance Calculator

What you still owe, which is never what you would guess

Ask someone eight years into a twenty five year loan how much is left and most will reason it out roughly: eight of twenty five is about a third, so around two thirds remaining.

They will be badly wrong, and always in the same direction.

This calculator gives you the actual figure. Tell it the original loan, the rate, the full term and how long has passed, and it works out the balance still outstanding at that point.

The gap between the guess and the answer is the whole reason the tool exists. Time passes evenly. Loan balances do not fall evenly, and the difference between those two facts is where a lot of financial planning quietly goes wrong.

Four boxes and two dropdowns

1. Loan. The amount originally borrowed, not the current balance. Working out the current balance is what this does.
2. Interest rate. The annual rate as a percentage.
3. Loan term. The full original term, with a dropdown for the unit.
4. Period. How much time has passed since the loan started, with its own unit dropdown.

One habit makes this much smoother: set both dropdowns to the same unit. If you have a 5 year loan and 18 months have passed, enter 60 months and 18 months rather than 5 years and 18 months. Same answer, and the two figures sit on a common scale so you can see at a glance that one is comfortably inside the other.

The dropdowns run from years all the way down to seconds. Nobody has a loan measured in seconds, and the wide range is there because the underlying converter is general purpose. Months and years are what you want.

The result comes back as a single figure, the loan remaining, with no currency symbol attached, so it is returned in whatever units you entered.

The backward looking method

There are two established ways to work out what is left on a loan, and this one uses what financial mathematics calls the retrospective method. It looks backward.

The idea is simple once stated. Take the original loan and roll it forward with interest as if you had paid nothing at all. Then take every payment you actually made and roll each of those forward with interest too. Subtract the second from the first, and what remains is what you still owe.

Balance = L × (1 + i)^p - M × ((1 + i)^p - 1) ÷ i

where L is the original loan, i is the monthly rate, p is the number of payments made, and M is the monthly payment.

The calculator works M out for itself first, from the loan, the rate and the full term, using the standard amortising formula. So you do not have to know your payment, which is convenient, because the number of people who know their exact payment to the cent is smaller than you would think.

Two sanity checks are built into the formula. At zero payments made, the balance is the original loan. At the end of the term, it is exactly zero. Everything in between is the curve, and the curve is the interesting part.

A 300,000 loan, checked at six points

Loan 300,000, rate 6 percent, term 30 years. The monthly payment works out to 1,798.65, and the calculator derives that on its own.

Ten years in, a third of the way through the term, you have cleared 16.31 percent of what you borrowed. You have paid roughly 215,838 into the loan over that decade, and it has reduced the debt by 48,943.

At the fifteen year mark, exactly halfway, the balance is 213,146. Twenty nine percent repaid.

The other seventy one percent disappears in the second half, and most of it in the last ten years.

Why the first years barely move it

None of that is a quirk of this particular loan. It falls straight out of how interest works.

Interest is charged on what you currently owe. At the start you owe nearly everything, so nearly all of the interest bill exists, and your payment has to clear it before a single unit touches the principal.

On the loan above, the first month's interest is 300,000 × 0.005 = 1,500. Your payment is 1,798.65. So 298.65 reduces the debt, which is under seventeen percent of what you paid.

The following month the balance is fractionally smaller, so the interest is fractionally smaller, so fractionally more goes at the principal. Repeat 360 times and you get a curve that starts almost flat and steepens all the way to the end.

Two practical consequences worth carrying.

Early years build very little equity. If you plan to sell or refinance within five years, the balance will still be close to the original loan, and your equity will come from whatever the property gained in value rather than from anything you repaid.

Extra payments are worth far more early. Anything you knock off the balance in year two stops generating interest for the twenty eight years that follow. The same amount in year twenty eight has almost no time left to work. If you want to see what that does to the finish date, the loan payoff calculator takes a payment and counts the months.

Two ways to reach the same balance

Worth knowing that this figure can be arrived at from either direction, and that the two agree.

The retrospective route, used here, looks backward: what the loan grew to, minus what your payments grew to.

The prospective route looks forward: the balance is simply the present value of all the payments you have left to make. Take your remaining payments, discount each back to today at the loan rate, add them up.

They sound like different quantities and they are provably identical. Which is a genuinely useful fact rather than a curiosity, because it gives you a way to check any balance figure you are given.

If a lender tells you the payoff on a 30 year loan after 10 years is 251,057, you can test it forward: 240 remaining payments of 1,798.65, discounted at 6 percent, should come to the same number. If it does not, something in the loan is not what you were told, and the usual explanations are fees added along the way, a rate that moved, or missed payments capitalised into the balance.

Four reasons to want this number

Checking a statement. Run your loan and compare against what your lender says. Small differences are normal, covered in the next section. Large ones are worth a phone call.

Working out your equity. Equity is what the asset is worth minus what you owe on it. The second half of that is exactly this figure, and it is usually the half people estimate rather than calculate. Once you have it, the LTV calculator will turn it into the percentage a lender cares about.

Deciding whether to refinance. Any refinancing conversation starts with the outstanding balance, since that is what a new lender would be lending you. Knowing it before you start the conversation puts you in a better position in it.

Planning a sale. Sale price, minus what you still owe, minus selling costs, is what actually reaches you. People routinely plan around the first number alone and are surprised by the third.

Why your statement may not match exactly

The figure here assumes a clean loan: a fixed rate for the whole term, every payment made on time and in full, nothing extra, no fees added along the way. Real loans wander from that, and here is where the differences usually come from.

You paid extra at some point. Even one additional payment puts your real balance below the schedule, and it stays below for the rest of the loan.

The rate moved. On a floating or adjustable loan, the payment and the path both change when the rate does. This models one rate throughout.

The first period was odd. Many loans have a gap between drawdown and the first full payment, which shifts everything slightly.

Fees were capitalised. Charges added to the balance rather than billed separately raise it above the schedule.

Your statement includes things this does not. Escrow for tax and insurance, or an insurance premium collected alongside the payment, are not part of the loan and do not belong in this comparison. Compare principal against principal.

A gap of a few units is rounding and timing. A gap of a few percent has a cause, and it is worth finding out which of the above it is.

Questions people ask

Do I enter my original loan or my current balance?

The original loan amount, along with the original full term. The current balance is what the calculator works out for you.

Which units should I use for the term and the period?

The same one in both dropdowns. For a 5 year loan with 18 months elapsed, enter 60 months and 18 months. It keeps both figures on a common scale and makes the comparison obvious.

Halfway through the term, is half the loan repaid?

Nowhere near. On a 300,000 loan at 6 percent over 30 years, fifteen years in you have repaid about 29 percent. The balance falls slowly at first and quickly at the end.

Why does the balance drop so slowly in the early years?

Because interest is charged on what you owe, and at the start you owe almost all of it. On that same loan the first payment is 1,500 of interest and only 298.65 of principal.

Do I need to know my monthly payment?

No. The calculator derives it from the loan amount, rate and full term before working out the balance.

Does it account for extra payments I have made?

No, it follows the original schedule. If you have overpaid, your real balance will be lower than the figure shown. The loan payoff calculator handles a changed payment amount.

How do I turn this into my equity?

Subtract the balance from what the asset is worth today. For the percentage a lender uses, the LTV calculator takes the balance and the value and returns the loan to value ratio.

My lender says a different number. Who is right?

Probably both. Extra payments, a rate change, capitalised fees, or an odd first period will all move the real balance away from the clean schedule. Small differences are rounding and timing. Large ones have a specific cause worth identifying.

References

The outstanding balance is computed by the retrospective method, under which the balance at a point in time is the accumulated value of the original loan less the accumulated value of the payments made to that date. The prospective method, which values the remaining payments instead, is mathematically equivalent. Both are set out in university financial mathematics materials for the actuarial syllabus. The amortising payment relation used to derive the instalment, and the actuarial method under which the unpaid balance is increased each period by the finance charge earned and reduced by the payment made, follow Regulation Z.

1. J. Robert Buchanan, Millersville University, Loan Repayment, MATH 372 Financial Mathematics I. https://sites.millersville.edu/rbuchanan/math372/LoanRepayment-handout.pdf
2. Miguel A. Arcones, Binghamton University, Manual for SOA Exam FM, Chapter 4: Amortization and Sinking Funds, Section 4.1 Amortization Schedules. https://people.math.binghamton.edu/arcones/exam-fm/sect-4-1.pdf
3. King Saud University, Department of Mathematics, Financial Mathematics ACTU 371, Chapter 3: Loans. https://faculty.ksu.edu.sa/sites/default/files/ACTU371_CH3_Loan.pdf
4. Consumer Financial Protection Bureau (CFPB), Regulation Z, Appendix J to Part 1026: Annual Percentage Rate Computations for Closed-End Credit Transactions. https://www.consumerfinance.gov/rules-policy/regulations/1026/j/