The monthly payment stays the same, but the split between interest and principal inside it changes every month.

Experiment

Hands-on experiment

Predict first — borrow $300k at 4% for 30 years and the monthly payment is about $1,432. In month one, how much of that reduces your principal?

Pay it month by month yourself ($300k · 4% · 30yrs)

Read more — why it exists · insights · common mistakes · formulasExpand ▾

Why

Why does this exist?

A $300,000 mortgage at 4% for 30 years. What's the monthly payment, and what's the total interest over 30 years? Most people sign the biggest contract of their lives without this calculation.

An amortized loan means paying the same amount every month. But look inside: early on, most of it is interest, and the principal shrinks only a little — because interest is charged on the remaining balance, which is largest at the start.

Not knowing this structure leads to the bewildered 'I've paid for years — why is the principal barely down?', and to misjudgments about early repayment, rate comparisons, and term choices.

Misconception

Common misconceptions

Same payment every month, so the principal shrinks at the same speed every month.

✓

Early payments are mostly interest. At $300k, 4%, 30 years, roughly $1,000 of the first $1,432 payment is interest — the principal drops only about $432. The principal only starts falling in earnest in the later years.

A 1%p rate difference is no big deal.

✓

On $300k over 30 years, going from 4% to 5% pushes total interest from about $216,000 to $280,000. One percentage point makes a difference of over $60,000.

Formula

Writing it as math

The reason the interest/principal split changes despite a fixed payment: interest is proportional to the remaining balance. Here's that structure as formulas.

This month's interest

Interest is always the current remaining balance times the monthly rate. The more principal remains — i.e., early on — the bigger the interest.

The monthly payment (amortized)

The formula for repaying principal P in n equal monthly payments M. It looks complicated, but it just encodes 'each month, pay the interest, and whatever's left reduces the principal'.

The principal portion grows every month

M is fixed while interest shrinks monthly, so the principal portion grows monthly. That's why the two colors in the graph slowly traded places.

In Real Life

Where you meet it in real life

Choosing a mortgage

30 years vs 20, fixed vs variable — the trade-off between monthly payment and total interest can be compared with exactly this structure.

Timing early repayment

Interest is proportional to the remaining balance, so the same lump-sum prepayment saves the most interest when made early.

Interest-only vs amortized loans

The total-cost gap between interest-only loans (pay interest, then principal at maturity) and amortized loans is computed with the same principle.

Leases and installment plans

A car payment plan's 'monthly installment' uses the same formula. Unless it's genuinely 0% financing, the sticker price and the total you pay are different numbers.

Math Behind