How should a calculator reconcile a payment that cannot be split into equal cents?
Held constant: $100 principal, three monthly periods, 0% interest and no fees.
A zero-interest example is a useful way to test a loan calculator. No interest formula should be needed: $100 divided by three is $33.333333… . But actual payments in this model are expressed in cents. That means three identical $33.33 payments would leave one cent unpaid.
| Month | Payment | Interest | Closing balance |
|---|---|---|---|
| 1 | $33.33 | $0.00 | $66.67 |
| 2 | $33.33 | $0.00 | $33.34 |
| 3 | $33.34 | $0.00 | $0.00 |
Download this example’s CSV · Load the inputs in the calculator
Track the unpaid cent
After the first $33.33 payment, the balance is $66.67. After the second, it is $33.34. The final payment is therefore $33.34, clearing the balance without interest. Total paid is exactly $100. A display that silently repeats $33.33 three times while claiming a zero balance would hide the discrepancy.
What our calculator rounds
The scheduled monthly payment and each monthly interest charge are rounded to cents. Loan balances are also maintained at cent precision. The final payment is adjusted to the remaining balance plus final interest. This is an explicit model choice; it is not a claim that every lender uses the same convention.
Why the zero-rate branch matters
The usual payment formula divides by an expression that becomes zero when the rate is zero. A reliable implementation handles this case directly with principal divided by months, then builds the payment schedule. Entering 0% should not produce NaN, an infinite result or an empty table.
Test an oversized extra payment
Starting from the same $100 example, set extra monthly principal to $1,000. The first payment should be capped at $100, and the table should stop after one month. No negative balance or artificial refund should appear. This boundary check is as useful as testing a typical larger loan.
Use the check carefully
Zero interest here means a numeric 0% input with no fees. A marketed “0%” offer can still include conditions or other charges that this calculator does not model. The example establishes arithmetic behavior only. Download the schedule, sum the Payment column and check that the sum of Principal also equals $100.
Rounding the regular payment does not eliminate the remaining cent. The last payment must reconcile the balance.
Check your understanding
What would five equal payments of this $100 loan be at 0%?
Show the reasoning
Exactly $20 each. No fractional-cent remainder is left, and total principal repaid remains $100.