Loan and mortgage repayment calculator

Most mortgages and personal loans are repaid in equal monthly instalments, which is known as an annuity. At the start most of each payment goes on interest and only a small part on the debt itself; towards the end it is the other way round. The bank sets the repayment so that the debt is exactly zero after the last one. Someone who borrows £400,000 over 30 years at 5% pays just under £2,150 a month, and pays the bank back over £770,000 over the whole period.

The calculator works the way banks do: interest is added monthly, and the monthly rate is one twelfth of the annual rate. Why this is not quite exact mathematically is explained in the article on how to work out mortgage interest.

How it works

The calculator works out the monthly repayment with this formula:

$$s=U\cdot \frac{i}{1-(1+i{)}^{-N}}$$

Here U is the amount borrowed, i the monthly interest rate as a decimal (the annual rate in per cent divided by 1,200) and N the number of monthly repayments.

An annual rate of 5% is $i=\frac{5}{1200}\approx 0.004167$ a month. Thirty years is 360 repayments. Substituting:

$$s=\mathrm{400,000}\cdot \frac{0.004167}{1-{1.004167}^{-360}}$$

The power 1.004167⁻³⁶⁰ comes to about 0.2238, so the denominator is 0.7762 and the repayment is £2,147.29. Over 360 months you will pay

$$360\cdot \mathrm{2,147.29}\approx \text{£}773023.14,$$

so the interest comes to £373,023.14, almost as much as you borrowed. In the first month the interest is 400,000 · 0.004167 ≈ 1,667, or £1,667, and only just under £481 of the repayment goes towards the debt.

The actual repayment may differ from the calculator’s by a few pounds, because banks round the repayment and adjust the last one. Banks sometimes also add fees and insurance, and the calculator does not include these. With a zero interest rate, the calculator simply divides the debt into equal parts.