Confused by the Merchant’s Rule for loans with partial payments? Learn how simple interest settlement works, step by step
The Merchant’s Rule finds simple interest on the entire original loan amount, and on every partial payment, all up to the final settlement date. You grow interest on the principal, grow interest on each payment, then subtract the payments from the principal to get the amount you really owe.
I will never forget the day Merchant’s Rule first made my brain explode. I was in 11th grade business math class, 8:00 in the morning, when my “obvious” 6,000 dollar loan with 2 partial payments homework problems was proved wrong.
If you’ve found yourself here because you’re trying to do computations along the lines of Contracts or because a client just paid down a note prematurely and you want to close out its balance properly, welcome. You’re not the only one. Let’s work through this complicated mess together one step at a time as I wish someone would have explained it to me long ago.
So… Then What Is the Merchant’s Rule?
In simple terms: the Merchant’s Rule is a formula for figuring simple interest on a loan that is paid (in whole or in part) before the actual due date of payment.
One step further: rather than pay down the balance immediately upon receipt of any payment, this fund keeps the original principal and every partial payment “growing” with interest until the last day of the settlement.
Then you pay it all off.
Determine the amount that the principal increases with interest from the date of commencement to the date of settlement. For each payment, work out how much it “would have grown” by from its payment date to the settlement date. Subtract step 2 total from step 1 total. What is left is the amount still owed.
It sounds strange at first why would a payment accrue interest in the months it’s already been given by the borrower? When you work it out with the actual figures, it makes sense. Honestly.
Just a friendly warning: if you came to this page seeking an explanation of payment-processing “merchant rules”, the rules that allow or block credit card transactions at particular types of retail stores, that’s a different subject entirely. This article is about the classic simple-interest debt-settlement method taught in business math and finance classes. That’s probably what you found via search.
How Does This Method Come Into Being?
Almost immediately, simple interest becomes complex once you start to make partial payments. Do you apply the interest to the balance at once when a payment is received? Or do you wait until the payment deadline?
Different lending conventions handle this in different ways and that’s why we have multiple competing approaches: The US Rule immediately applies any payment to interest first and then principal when received by the lender.
(A variation: if a defaulting payment is too small to cover the subsequent payment’s accrued interest, then it’s not applied in installments, but instead piques until its due payment solution all remaining interest.) The Merchant’s Rule is to set off everything at the last settlement date.
Banker’s Rule is a whole other thing; it applies 360 days to a year for simple interest and it treats partial payments quite differently.The merchants Rule seems to occur most frequently in promissory notes, short-term commercial loans, and installment settlements, which the parties to the transaction pre-agree to settle in full at the conclusion.
My best hypothesis on why it is called the Merchants Rule (which may be wrong or confounded by other terms of art) is that merchants managing multiple running accounts may have preferred to perform a single clean settlement calculation rather than reconciling the books after every payment. I have not been able to locate a definitive etymology of the phrase, so I offer this simply as a hypothesis.
An Example That Finally Made Sense to Me
Let’s go through actual numbers as quickly as possible to really understand this. This is basically the exact problem that kept me up all night in college.
The situation: You borrow $6000 at 6% for 4 years with simple interest. You make one partial payment of $3000 at the end of year 2 and another of $3000 at the end of year 3. At the end of year 4, what do you owe (settlement)? Here’s how the Merchant’s Rule solves it:
Step 1: accumulate the up-to-date principal of the trade to the settlement date, get the full $6,000 and figure simple interest on it for the full 4-year term, assuming the borrower never makes a payment.
Principal with interest = $6,000 (1 + 0.064) = $6,000 x 1.24 = $7,4405.
2 To find the interest that needs to be repaid, we use the formula:Principle with interestdue = dollar amount a person needs to reinvest x [1 + (interest rate/2) x number of 6 month periods in the investment]10 dollars sum of money needed to reinvest x [1 + (7.7percent/2) x number of 6 month periods in the investment]
Step 2: for each payment, accumulate interest to the date of settling.
It is necessary to know what kind of interest accrues (e.g. ordinary or exact interest). Since the date of settling, which is the second date, is not fixed, this step does not proceed straightforwardly.
This is where everyone gets confused. Imagine that each produced interest from the day it was paid by the borrower until the settlement date using the forward method, not the backward one.
First payment ($3 000 paid at year 2, so has 2 years left to settlement): $3,000(1+0.062) = $3,0001.12 = $3,360
Second payment (‘3 000 paid at year 3 so it has 1 year to be paid): ‘3,000 (1 + 0. 06 1) = ‘3,000 (1. 06) = ‘3,180
Step 3: Deduct the grown payments from the increased principal.
Settlement Balance= $7440 ‘ $3360 ‘ $3180 = $900
You have a final bill of $900 at the end of year 4, not the flat $0 you might have guessed from $3,000 + $3,000 and simply halting. (I made that very mistake in the first go-around.)
The interest keeps compound-compounding on every dollar, on each side of the scoreboard, until the final day.
Imagine a footrace: individuals may be starting at different points on the course but all need to reach the same point at the end. The principal has a long head start in the race (day one), which means it gains the most ‘distance’ (interest).
Individual payments start partway along the course (contributing interest only for the portion of the course it still has to go), and the individual finishing in front (principal or payments) determines who owes who.
Merchant’s Rule, When Compared to the U.S. Rule, What Is the Difference?
I have made this mistake on an exam before, so here is another stab at it to ensure you get it.
| Feature | Merchant’s Rule | U.S. Rule |
| For payments applying | If the entry is debtor then it is treated as a debit to the account whereas if it is a creditor then it is considered as a credit. | Netted out (at the final settlement date) applied immediately once the lender has been paid. |
| Interest on payments | payments continue to accrue interest until the time of settlement. | Once you’ve paid your regular obligations, and when you have the cash available, you must use your payment too. |
| Typical use case | For most of his work in his domain, the user will want to use the application by performing several common tasks or work flows, which fall under the umbrella of a typical use case. Such use cases should be very familiar to the user, because they are a natural part of what he would do in his domain without computers. | Business notes were calculated with one lump sum. |
| Federal rules, consumer lending. Most of the federal rules apply to consumer credit, that is most consumer loans in the U.S. even if the loans are due. They are specific to loan servicing. | ||
| Slightly more | theoretically oriented, sometimes involves less total steps more intuitive, but have to recalculate each time a payment is made | |
| Who it benefits | May favor the lender to a small extent based on when payments are made | the standard-downside, borrower-friendly, legally routine method in the U.S. |
Merchant’s Rule in Practice: Real-World Use and Practical Tips
Here’s the bottom line: right in the real world of United States lending, the United States Rule is what applies most of the time to most of the lawsuits over partial payments; it goes as far back as 1839 U.S. Supreme Court decision, Story v. Livingston, which determined that when a debtor makes a payment, the creditor computes interest.
So if you are doing your finance homework, you can expect the homework to require you to do both methods and then compare between the two.
Whereas if you are actually settling an actual note out in the real world, just check what method your loan agreement needs (it really does make a difference to the number you end up with).
Track the timing, not the order. Order doesn’t matter so far as interest accruing by itself is considered, but you need to keep very careful track of how much time is in between each payment date and the final settlement date (not the start date of the loan). Use simple interest.
The Merchant’s Rule sticks to simple interest all the way through. Slip into compound interest formulas by mistake and your figures will go awol very quickly, even over short time scales. Match your units of time.
For example, use years, months, or days, but keep the use of units consistent. I lost half the credit for using months in one part of the calculation but years elsewhere. Ouch I haven’t made that mistake again.
Build a quick table. When you have several or more payments to analyze, draw a table: payment amount, payment date, time remaining to settlement, and accumulated value. This takes an abstract word problem and makes it visually real.
When You’d Actually Use This in Real Life
Merchant’s Rule calculations show up in:
- Partial payments (premiers) of promissory notes settled among those enterprises that had committed partial payments before maturity.
- Trade credit from merchants (That’s why probably where the name derives from.
- Loan restructuring discussions where both sides prefer a ‘one lump sum, no amortization schedule.
- Qualification exams in business mathematics, accounting, and finance.
Having a shop and letting a customer run a tab? Payments come in sporadically to chip away the balance?
FAQs
Is the Merchant’s Rule Equivalent to Simple Interest?
It is based on simple interest but it takes care of multiple payments on a simple-interest loan not in an abstract interest calculation.
Which Is Best: Merchant’s Rule, or the U.S. Rule?
Wins neither are universally accepted; they’re merely different conventions. The U.S. Rule applies to a majority of consumer and legally regulated loans in the United States, while the Merchant’s Rule is seen more in particular business settlement agreements and in school work.
Is Compound Interest Applied by the Merchant’s Rule?
No. It works out the simple interest on the principal as well as on the payments (with the right time periods for each).
Could the Settlement Balance Ever Be Negative?
Yes. Again, this only works if the payment grown is greater than the principal grown, this means the borrower has overpaid.
Key Taking
- The Merchant’s Rule applies and computes simple interest on all monies the principal receives, and on each partial payment, until the time of settlement.
- If you then subtract the grown payments from the grown principal, you get what still remains to be paid.
- It is unlike the U.S. Rule, which applies a pmt directly to interest and then, the balance to principal immediately.
- It is most frequently employed in business notes, trade credit, and coursework on business-math. Besides, U.S. consumer and legally regulated loans generally conform to the US Rule.
Additional Resources:
- Introduction to Business Math (Chapter 5 Summary) eCampusOntario Pressbooks:a free, well-organized open textbook chapter covering simple interest, promissory notes, and related terminology.
- Investopedia: Simple Interest:a clear refresher on how simple interest works before tackling partial-payment methods like this one.
