Amortization Schedule Calculator

An amortization schedule is a table with one row per payment. Each row records the interest charged that period, the principal repaid, and the balance left over. The payment itself never changes; the split changes every single row.

The level payment comes from

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

with $P$ the principal, $r$ the periodic rate (annual rate $\div$ periods per year) and $n$ the number of payments. Then, row by row, starting from $B_0 = P$:

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

A correct schedule ends with $B_n = 0$ (to the cent). The whole table follows mechanically from those three lines — everything else, including the totals, is bookkeeping.

This page is a math tool. It shows the arithmetic on the numbers you enter; your actual lender's schedule depends on their rounding, fees and day-count conventions.

Closed forms you can use instead of the table

The remaining balance after $k$ payments, without building every row:

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

Total interest over the whole loan:

$\text{total interest} = nM - P$

And the number of payments needed to clear a balance at a chosen payment $M$:

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

That last one is how you price an extra payment: raise $M$, recompute $n$, compare $nM$ against the original.

Simple interest is a different animal

$I = P \cdot r_{\text{annual}} \cdot t$

Simple interest never touches the balance, so it always overstates the cost of an amortizing loan, where the balance falls every month. Use it only for instruments that genuinely accrue that way.

Why early payments feel wasted

$I_k$ is proportional to the balance, which is largest at the start. The crossover — the row where principal first exceeds interest — arrives later the longer the term and the higher the rate.

• Annual rate in a monthly row: $r$ must match the payment frequency. A 5% annual rate is $0.05/12 \approx 0.0041667$ per month.
• Charging interest on the original principal every row: interest is on the current balance $B_{k-1}$, which is the entire point of amortization.
• Rounding drift: rounding $M$ and every row to the cent leaves a small residue. Real lenders adjust the final payment to force the balance to exactly zero — never leave a schedule ending at -\0.07$.
• Confusing $n$ with years: a 30-year monthly loan has $n = 360$, not 30.
• Assuming an extra payment cuts interest proportionally: it does not. The saving depends on when it is made; the same dollar early is worth far more than late.
• Treating $nM - P$ as the cost of a loan paid off early: that total assumes every scheduled payment is made. Pay it off in month 40 of 60 and the interest total is much smaller.