Mortgage repayment calculator

What this works out

A repayment mortgage is a loan paid off by a level monthly payment, part of which is interest on what is still owed and part of which reduces the debt. The payment stays the same; the split moves, slowly, across the term.

Two things follow from that, and neither is obvious from the payment figure on its own. The first is how much the borrowing costs in total, which on a long term is frequently more than the amount borrowed. The second is how much of that disappears if you pay a little more each month, which is a far larger number than most people expect.

The method

The level payment comes from the standard annuity formula: the amount borrowed multiplied by the monthly rate, scaled so that exactly n payments bring the balance to zero. The tool then walks the balance down month by month rather than trusting the formula, because the schedule is what the visitor is actually being shown and it has to be the same arithmetic.

The monthly rate is a choice, and it is the reason two honest calculators disagree. Dividing the annual rate by twelve is what nearly every lender does. Taking the twelfth root of the annual rate is the basis behind an APRC and produces a slightly lower payment, because twelve months of compounding then come to exactly the annual figure rather than a little over it. Both are offered; the first is the default because it is what the paperwork will say.

Interest is charged on the balance at the start of the month and the payment is applied at the end, which is what the payment formula assumes. Interest is kept at full precision internally and rounded only for display, so the schedule depends on the rate rather than on a rounding rule.

The payment itself is rounded to the nearest penny, which is what a lender quotes. That leaves the schedule a few pounds over or short by the end of a 30-year term, and the final payment carries the difference — which is also what happens on a real mortgage, where the last payment is an adjustment rather than a copy of the other 359.

Overpayments are applied to the same schedule, shortening it. The contractual payment is not recalculated, because that is what lenders do by default. Every figure about overpaying on this page is the difference between two runs of the same function: the contractual schedule, and the one actually paid.

Before you read on

Borrow 300,000 at 6.5% over 30 years and the payment is 1,896.20 a month. How much of the first one comes off the debt?

• AAbout half of it.

  That comes true eventually — on this mortgage, in month 233.

• B271.20, under 15% of the payment.

  Yes. The other 1,625.00 is the first month's interest.

• C1,625.00.

  That is the interest, not the capital — the two halves the other way round.

271.20, which is 14% of it. Interest is charged on the balance at the start of the month, and at the start of the first month you owe the whole 300,000 — so 300,000 x 0.065 / 12 = 1,625.00 goes on interest before anything touches the debt. The share improves every month as the balance falls, but on the contractual schedule it does not pass half until month 233 of 360, and that asymmetry is the entire reason an overpayment early is worth so much more than the same money late.

• Interest1,62585.7%
• Off the debt271.214.3%

A worked example

The figures below carry no currency symbol on purpose: the arithmetic is the same in pounds, euros or dollars, and the tool follows whichever currency your locale uses.

Borrow 300,000 at 6.5% over 30 years, and pay 200 a month on top of the contractual payment.

Monthly repayment	1,896.20
Interest in the first payment	1,625.00
Interest over the term	279,186.15
Total repaid	579,186.15
Interest saved by overpaying	103,450.35
Term cut by	6 years 11 months
Cleared in	23 years 1 month

Without the overpayment the same mortgage runs the full 360 months and costs 382,636.50 in interest, for 682,636.50 repaid in all. So the extra 200 a month — 53,938.75 of it by the time the debt clears, since the final month is an adjustment rather than a full payment — removes 103,450.35 of interest.

Figure	Contractualno overpayment	Plus 200 a month	Difference
Paid each month	1,896.20	2,096.20	+200.00
Interest over the term	382,636.50	279,186.15better	−103,450.35
Total repaid	682,636.50	579,186.15better	−103,450.35
Time to clear	30 years	23 years 1 monthbetter	−6 years 11 months

The 200 buys back 103,450.35 of interest and nearly seven years, for 53,938.75 laid out — nearly two back for every one paid early. It works that well only because it is paid early: the same money in the final decade meets a balance that has almost no interest left on it.

Check the payment against the closed form:

i = 0.065 / 12 = 0.00541667
n = 30 x 12    = 360

(1 + i)^n = 6.991798

payment = 300,000 x 0.00541667 x 6.991798 / (6.991798 - 1)
        = 11,361.67 / 5.991798
        = 1,896.20

And the first payment splits as 300,000 x 0.00541667 = 1,625.00 of interest, leaving 1,896.20 - 1,625.00 = 271.20 off the debt — just under 86% of the first payment is interest, and on the contractual schedule it stays above half until month 233.

These are the same numbers asserted in this tool’s test file, so if the formula ever changes without this page changing with it, the build fails.

What it does not do

It assumes one rate for the whole term, which no fixed deal offers, and it prices capital and interest on the loan alone. Product fees, insurance, property tax and service charges are all on top, and a lender’s own illustration will include some of them. It does not model an interest-only period, a part-and-part mortgage, an offset account, a rate that tracks a base rate, or the early repayment charge most lenders apply above roughly 10% of the balance a year. Treat the overpayment figures as what is possible rather than what your particular deal permits, and check the charge before acting on them.

For a smaller balance over a shorter term — a car, a personal loan, a refit — loan repayment runs the identical formula without the property assumptions attached to it.

i = annual rate / 12          (or (1 + annual rate)^(1/12) - 1)
n = 12 x term in years

payment = P x i x (1 + i)^n / ((1 + i)^n - 1)

Then, for each month until the balance reaches zero:
  interest  = balance x i
  balance   = balance + interest - (payment + overpayment)

The final payment is whatever settles the balance, so it is
a few pounds different from all the others.

where
  P = amount borrowed, less any one-off overpayment
  i = the monthly interest rate
  n = the number of contractual payments