How the remaining balance is calculated
On an equal-installment loan, every monthly payment is the same amount, but the split between interest and principal shifts over time. The remaining balance after t months is the original loan amount grown at interest, minus what the t payments made so far have removed from it.
- P — loan principal
- r — monthly rate = annual rate / 12
- n — total number of payments = the total term, in months
- t — months elapsed so far
- M — fixed monthly payment
- B(t) — remaining balance after t months
Common values
| Loan principal (₩) | Remaining balance |
|---|---|
| 10,000,000 ₩ | ₩9,044,751 |
| 25,000,000 ₩ | ₩22,611,878 |
| 50,000,000 ₩ | ₩45,223,757 |
| 100,000,000 ₩ | ₩90,447,513 |
| 150,000,000 ₩ | ₩135,671,270 |
| 200,000,000 ₩ | ₩180,895,026 |
| 300,000,000 ₩ | ₩271,342,539 |
| 500,000,000 ₩ | ₩452,237,566 |
| 1,000,000,000 ₩ | ₩904,475,131 |
More detail
Why the balance falls slowly at first
Early monthly payments are mostly interest, because interest is charged on the full outstanding balance. As the balance shrinks, less of each payment goes to interest and more goes to principal — so at any rate above 0% the balance drops faster in the later years of the same loan, not evenly across the term. On 100,000,000 at 4% over 360 months the first payment retires 144,082 of principal and the last one retires 475,829 — 3.3 times as much. At exactly 0% there is no interest to shift, so every month retires the same 277,778 and the balance falls in a straight line.
Using this before a refinance or early payoff
Lenders often quote a payoff amount close to, but not identical to, this remaining balance — fees or per-diem interest can add a small amount. Use this figure to compare refinance offers or decide whether an early lump-sum payment is worth it, then confirm the exact payoff amount with your lender.
Money tip. The principal-paid-so-far figure above is a useful sanity check: on a long-term loan (25–30 years) at typical rates it can take most of the term before principal paid overtakes interest paid — at 4% over 30 years, about 24 years. Push the rate to 5.5% or higher and, on the same 30-year term, principal paid never catches up with interest paid at all before the loan ends — even though the monthly payment never changes.
Frequently asked questions
Why is my remaining balance still so close to the original loan amount after several years?
Because equal-installment payments are front-loaded with interest — the monthly payment M is fixed, but early on most of it covers interest on the still-large balance, so principal reduces slowly. Compare the principal-paid-so-far and interest-paid-so-far outputs above: on a 30-year loan, interest often exceeds principal paid for the first decade or more.
Does making the elapsed-months input larger always lower the remaining balance?
Yes, monotonically — every additional month applies another payment where at least part goes to principal, so B(t) strictly decreases as t rises from 0 (balance = full principal) to the total term (balance ≈ 0).
How is this different from just multiplying the monthly payment by the months elapsed?
Monthly payment × months elapsed gives the total amount paid so far, which includes both principal and interest. The remaining balance only tracks the principal portion left — it's the original loan minus principal-paid-so-far above, not minus the total amount paid.
What if the total term or elapsed months I enter isn't a whole number of years?
Enter both in months — the formula works with any month count, not just whole years, so a 42-month total term with 15 months elapsed works exactly the same as a 360-month term.