Loan Amortization Schedule Calculator

An amortization schedule is one row per payment: interest charged, principal repaid, balance left. The payment is constant, the split inside it is not.

First find the level payment:

$M = P \cdot \frac{i(1+i)^n}{(1+i)^n - 1}$

with $P$ the amount financed, $i$ the periodic rate (annual $\div$ 12 for monthly payments) and $n$ the number of payments. Then from $B_0 = P$, each row is

$I_k = B_{k-1} \cdot i, \qquad P_k = M - I_k, \qquad B_k = B_{k-1} - P_k$

Because $I_k$ is proportional to a balance that keeps falling, interest shrinks and principal grows every row. Two totals come straight out of the table:

$\text{total paid} = nM, \qquad \text{total interest} = nM - P$

Both assume the schedule is followed to the end. This page works the arithmetic on the numbers you enter; a lender's own schedule may differ slightly through their rounding and day-count conventions.

Balance at any row, in closed form

$B_k = P(1+i)^k - M \cdot \frac{(1+i)^k - 1}{i}$

That figure is the payoff principal after $k$ payments — no table required.

What an extra payment buys

Raising the payment shortens the term. Solve the annuity equation for $n$:

$n = \frac{-\ln\!\left(1 - \dfrac{iP}{M}\right)}{\ln(1+i)}$

Compare $nM$ before and after; the difference is the interest saved. Note the constraint hidden in the logarithm: if $M \le iP$ the payment never covers the interest, the bracket goes non-positive, and the loan never amortises at all.

Per-diem interest

Between scheduled dates, interest usually accrues daily:

$\text{per diem} = \frac{B \times r_{\text{annual}}}{365}$

A payoff quote is the balance plus per-diem interest to the settlement date. Some agreements use a 360-day year and some charge fees on early settlement — those terms are in your contract, not in this formula.

Why timing beats size

The same extra dollar paid in month 3 removes far more interest than in month 50, because it removes interest from every remaining row.

• Annual rate in a monthly row: $i$ must match the payment frequency. 7% annual is $0.07/12 \approx 0.0058333$ per month.
• Applying interest to the original principal: $I_k$ uses $B_{k-1}$. Using $P$ every row turns an amortising loan into simple interest and overstates the cost badly.
• Assuming extra payments cut interest proportionally: a 20% larger payment does not save 20% of the interest. The saving depends on how much term it removes and when.
• Confusing the payoff amount with the remaining payments: the payoff is $B_k$ (plus accrued per-diem), not the sum of what is left on the schedule. That sum includes interest that will never be charged.
• Rounding drift: rounding $M$ and every row leaves a residue of a few cents, which lenders absorb in the final payment.
• Forgetting to re-round the term: a computed $n$ of $49.36$ means 50 payments, the last one smaller than the rest.