Loan Payoff Calculator

The question most loan calculators dodge

Nearly every loan tool assumes you know the term. Enter the years, get the payment. Fine if you are being offered a loan.

Not much use if you already have one and the real question is when it ends. Or if you have decided what you can afford each month and want to know what that buys you.

This one runs that way round. Give it the balance, the rate, and the payment you intend to make, and it counts how many payments it takes to reach zero. Then it prints every one of them, so you can see exactly where the money goes on the way.

It is also the honest way to test an idea. Anyone can say they will pay a bit extra. Watching thirty six payments disappear off the end of the schedule is what makes the idea stick.

Three fields

1. Loan Amount. What you owe right now, not what you originally borrowed. Your current balance is the number that matters.
2. Payment Amount. What you will pay each month, in total. If you plan to overpay, put the full amount here rather than just the extra.
3. Interest Rate. The annual rate as a percentage.

Press Calculate and you get the number of payments, followed by the full schedule: for every month, the opening balance, the payment, how much of it was interest, how much came off the principal, your running totals of both, and the balance left afterwards.

Note that this works in monthly payments. If your loan is on some other schedule, the loan payment calculator handles quarterly and annual instalments.

Why a payment can be too small to ever finish

Enter a payment that is too low and the calculator refuses, and tells you exactly why: the payment does not cover the interest, so the loan will never be paid off.

That is not the tool being fussy. It is arithmetic, and it is worth understanding because it is how people end up trapped.

Every month, interest is added to what you owe. Your payment goes at that interest first, and only what survives touches the principal. So if the payment is smaller than the month's interest, nothing touches the principal at all. Worse, the shortfall gets added on, and next month's interest is charged on a larger balance than this month's.

The balance does not stall. It grows, and it grows faster every month, while you make payments the whole time.

On a 10,000 balance at 7 percent, the first month's interest is 10,000 × 0.07 ÷ 12 = 58.33. Pay 58.33 exactly and the balance never moves, no matter how long you keep going. Pay less and it climbs.

So there is a floor under every loan, and it is simply the current balance multiplied by the monthly rate. Any payment must clear that before it does you the slightest good. If you have ever wondered how someone pays a credit card for years and owes more than they started with, that is the entire mechanism.

The calculator also stops if a payment would take more than a hundred years to clear the balance, which catches the cases that technically work and practically do not.

It counts rather than calculates

There is a formula for the number of payments, involving logarithms, and it works when everything is tidy. This tool does not use it. It simulates the loan month by month instead.

Three steps, repeated:

1. Interest for the month is the current balance multiplied by the monthly rate, which is your annual rate divided by twelve.
2. Whatever the payment has left after covering that interest comes off the balance.
3. If the balance has reached zero, stop and count. Otherwise carry the new balance into the next month.

The final payment gets trimmed to whatever is actually left, so the loan closes at exactly zero rather than overshooting into a negative balance.

Simulating rather than solving costs nothing and buys two things. You get the whole schedule as a by-product, rather than a lone number. And the running total of interest is summed from the actual months rather than estimated, which is the more careful of the two ways to arrive at it.

One pleasant consequence: this handles a zero percent loan without complaint. The formula-based approach divides by the rate and falls over, while a simulation simply finds there is no interest to cover and puts the whole payment against the principal.

Ten thousand at seven percent, a hundred a month

Balance 10,000, rate 7 percent, payment 100.

The monthly rate is 7 ÷ 12 = 0.5833 percent. So the first month's interest is 58.33, and of your 100, only 41.67 reduces what you owe.

Fifty eight percent of your first payment is rent on the money.

The calculator runs it forward and lands on 151 payments. Twelve years and seven months, to clear ten thousand at a hundred a month.

Total interest across those years is 5,051.84, so you repay 15,051.84 in all. Borrowing ten thousand cost you half as much again.

The last payment is the mirror of the first: 0.30 of interest and 51.54 of principal. By then the balance is tiny, so there is almost nothing for the rate to bite on.

What makes this example useful is how ordinary it looks. Seven percent is not a punishing rate. A hundred a month is not a careless payment. And it still takes over twelve years and costs half the loan again, because the payment is small relative to the balance and most of the early years go on interest.

What another twenty a month does

Same loan, same rate, and the payment nudged upward:

Going from 100 to 120 is twenty percent more out of your account. It removes 36 payments and saves 1,316.45 in interest.

Read that again, because the ratio is the point. An extra 20 a month, which is 2,300 across the shortened life of the loan, buys you three years and over thirteen hundred of interest you never pay.

Doubling the payment to 200 more than halves the time and cuts the interest by nearly two thirds.

The reason the returns are so lopsided is that every extra amount goes entirely against the principal. Your required payment is already covering the interest, so the extra has nothing to fight. It removes balance immediately, and that removed balance stops generating interest for every remaining month of the loan.

Which is why small, early and consistent beats large and eventual. Twenty a month starting now generally does more than a hundred a month starting in three years.

Reading the schedule it prints

The table has eight columns and most people glance at it once. Three of them repay attention.

Interest against Principal, in the early rows. This is where you find out what proportion of your payment is actually working. If interest is taking more than half, the loan is expensive relative to what you are paying against it, and either the rate or the payment deserves a look.

The month those two columns cross. Somewhere in the schedule, the principal column overtakes the interest column. Everything before that point is a loan that mostly costs you money. Everything after is a loan you are mostly repaying. On short, well-paid loans it happens almost immediately. On long ones it can take years.

Cumulative Interest, at the bottom. The final row of that column is the total price of the loan. It is the number to compare against alternatives, and the number to look at before agreeing to extend a term.

A practical use: run your existing loan, find the row for the month you are in now, and compare the ending balance against your latest statement. If they are close, the schedule is a reliable map of what is ahead. If your real balance is lower, you have been paying more than you thought, which is worth knowing.

Pointing it at the right debt first

If you have several debts and some spare money each month, the order you attack them in matters more than the amount.

Run each debt through here twice, once at the current payment and once with the extra added. The one where the extra removes the most interest is mathematically the right target, and it will almost always be the debt with the highest rate rather than the largest balance.

That is worth stating plainly because instinct says otherwise. A large loan feels more urgent than a small one. But interest is charged as a percentage, so a 3,000 balance at 24 percent is generating more cost per month than a 20,000 balance at 6 percent, and clearing the small expensive one first frees up more money faster.

There is a counter-argument worth respecting. Some people do better clearing the smallest balance first, whatever the rate, because finishing something is motivating and a debt that disappears entirely frees its whole payment. That approach costs slightly more in interest and works better for some households than the optimal one they abandon in month four. The calculator will show you the price of choosing it, and then it is your call.

Questions people ask

What does this calculate?

How many monthly payments it takes to clear a loan, given the balance, the annual rate and the payment you intend to make. It also prints the full month by month schedule.

Do I enter the original loan or my current balance?

Your current balance. The schedule runs forward from wherever you are now, so entering the original amount answers a question about a loan you no longer have.

Why did it say my payment is too low?

Because the payment does not cover the monthly interest, so the balance would grow rather than shrink. The floor is your balance multiplied by the monthly rate. On 10,000 at 7 percent that is 58.33, and any payment at or below it never clears the loan.

How do I model overpaying?

Enter your total intended payment, not just the extra part. If your required payment is 100 and you plan to add 50, enter 150.

Does it handle a zero percent loan?

Yes. With no interest to cover, the whole payment goes against the principal, and the number of payments is simply the balance divided by the payment, rounded up.

Can I use it for fortnightly or quarterly payments?

The schedule is monthly. For quarterly or annual instalments the loan payment calculator handles other frequencies, and for a mortgage the amortization calculator prints a dated schedule.

Does it include fees or insurance?

No. It models the loan itself. Processing charges, insurance premiums and any other amounts collected alongside your payment sit outside the schedule, so enter only the part that goes against the loan.

Which debt should I clear first?

Usually the one with the highest interest rate, since that is where each extra unit removes the most cost, regardless of balance size. Run each debt with and without the extra payment and compare the interest saved.

References

The month by month method used here is the standard amortisation approach, under which each payment first offsets the interest accrued since the previous payment and the remainder reduces the outstanding principal, as set out in university financial mathematics materials for the actuarial syllabus and in Regulation Z, which describes the actuarial method in the same terms and publishes its equations so they can be used to program calculators.

1. 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
2. J. Robert Buchanan, Millersville University, Loan Repayment, MATH 372 Financial Mathematics I. https://sites.millersville.edu/rbuchanan/math372/LoanRepayment-handout.pdf
3. 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/
4. Consumer Financial Protection Bureau (CFPB), Regulation Z, § 1026.22 Determination of Annual Percentage Rate. https://www.consumerfinance.gov/rules-policy/regulations/1026/22/