Loan Calculator

How a loan payment is worked out

An amortizing loan is repaid with one fixed monthly payment that covers both the interest owed that month and a slice of the principal. Early on, most of the payment is interest because the balance is large; as the balance falls, the interest shrinks and more of each payment goes to principal. The size of that fixed payment comes from the annuity formula: payment = P · r(1+r)^n / ((1+r)^n − 1), where P is the amount borrowed, r is the monthly rate (annual rate ÷ 12) and n is the number of monthly payments.

Worked example: 200,000 at 6% for 30 years

With P = 200000.00, r = 0.06 / 12 = 0.005 and n = 360, the formula gives a payment of 1199.10 a month — the exact figure lenders quote for these inputs. In the first month the interest is 200000.00 × 0.005 = 1000.00, so only 199.10 of that first payment reduces the balance. Thirty years later the roles have flipped and almost the whole payment is principal. Over the full term you pay about 231,677 in interest — more than the amount borrowed — which is why the rate and the term matter so much. Cut the term to 15 years and the monthly payment rises but the total interest falls sharply, because the balance spends far less time accruing.

Why the schedule is built in exact cents

Money only exists in whole cents, and a naïve calculator that carries fractional cents in floating-point drifts: after 360 rounded interest charges and 360 rounded payments, the ending balance can miss zero by a few cents, and the principal portions no longer add up to what you borrowed. This tool avoids that entirely. Every amount is an integer number of cents; each month the interest is rounded to the nearest cent, the principal portion is the payment minus that interest, and the balance is reduced by an exact integer. The final payment is then set to exactly the remaining balance plus its interest, so the loan closes at precisely 0.00 and the principal columns sum to the original amount to the cent. That is why the last payment is often a cent or two different from all the others — it absorbs the accumulated rounding, which is exactly what a real lender's final statement does.

Extra payments and early payoff

Anything you pay beyond the required monthly payment goes straight at the principal, and a smaller principal accrues less interest from the very next month — that is the entire mechanism, and it compounds in your favour for the rest of the loan. This tool models it the simple, common way: every extra amount is applied to principal at payment time, on top of the unchanged regular payment, so the loan simply ends sooner. You can add a recurring extra per month, a one-time lump sum at a chosen payment number, or both, and the savings readout compares the result against the same loan with no extras: the new payoff point, the months saved, and the interest saved — all computed in exact integer cents, never estimated from a formula.

The numbers are bigger than most people expect. On the 200,000-at-6%-for-30-years example, an extra 200.00 a month (17% more than the 1199.10 payment) retires the loan after 252 payments instead of 360 — 9 years early — and cuts total interest from 231,677.04 to 151,876.18, a saving of 79,800.86. A single 10,000.00 lump sum at payment 12 saves 41,044.36 of interest and 42 months, because that principal would otherwise have accrued interest for nearly three decades. Extras early in the loan save far more than the same extras late, when most of the interest has already been paid.

Two honest caveats. First, in the closing month the extra is capped at exactly what remains, so the schedule never shows you overpaying — the final payment still lands the balance on precisely 0.00. Second, real lenders vary: some re-amortize (recast) after a lump sum to lower the payment instead of shortening the term, some apply extras to next month's payment rather than to principal unless told otherwise, and a few charge prepayment penalties. This tool models none of that — it assumes the plain principal-reduction treatment, which is the default for most modern mortgages and consumer loans in the US and EU, but read your own loan's prepayment terms before counting the savings.

Zero-percent loans

Promotional 0% financing is a real and common case, and the annuity formula divides by zero at that rate. Rather than blow up, the tool splits the principal evenly across the term: the payment is principal ÷ months with no interest anywhere. When the division is not exact — 100.00 over three months, for instance — you get 33.33, 33.33 and a final 33.34, so the payments still total exactly the principal and the balance still lands on zero.

Reading the schedule and exporting it

The table lists every payment with its number, amount, the part going to principal, the part going to interest, and the balance left afterwards. Watch the interest column fall and the principal column rise row by row — that crossover is the whole story of amortization. Copy schedule as CSV copies the entire table (header plus one row per payment) as plain comma-separated decimals with no currency symbol or grouping, so it pastes straight into a spreadsheet or a script. With extra payments on, both the table and the CSV gain an Extra column showing exactly how much of each payment went to principal on top of the regular amount.

Honest limits

This is arithmetic, not a loan quote or financial advice. It computes principal and interest only, treating the rate you enter as a simple nominal annual rate compounded monthly (1/12 per month). It does not add property tax, insurance, HOA fees, origination or closing costs, and it does not compute a regulatory APR, which folds certain fees into an effective rate and will usually be a little higher than the note rate. Real lenders also use exact-day interest conventions rather than a flat month, so a bank's statement can differ by small amounts. And it assumes a fixed rate throughout — a variable-rate loan or an interest-only period would change the schedule. Extra payments are modeled as plain principal reduction at payment time (see above); lender-specific recast, redirection or prepayment-penalty rules are not. Use it to understand the shape of a loan and compare scenarios, then confirm the exact numbers with the lender.