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According to the general repayment formula, the mortgage repayment for month j is calculated by \begin{equation} Rj = \frac{L_{j-1}x_j}{1-(1+x_j)^{-(N-(j-1))}}. \end{equation} where $L_{j-1}$ is the loan amount outstanding from last month, $x_j$ is the interest rate in month j and N is the number of months the original mortgage was for.

Why, if the interest rate stays the same, does the repayment not change? the loan amount that the interest is calculated on goes down and so does the length of time left on the mortgage so why is the end result still the same?

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    what do you mean by the end result stays the same - what does it stay the same with? As if you have a variable $x_j$ instead of $x_j=x$? – 2017-02-21
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    I mean the monthly repayment is still the same amount as it was the month before. Yes i have written a variable because it is possible that the interest rate will change at some point over the mortgage, but say it is fixed for some period, the repayment amount is equal for these periods – 2017-02-21
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    As the loan balance ($L$) declines the denominator is decreasing at the same rate, and the payments stay the same. Or, the equation is specifically engineered to create level payments over the life of the loan. – 2017-02-21
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    i meant a variable rate i.e non-constant rate rather than how you denote an unknown quantity. :) – 2017-02-21
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    Level coupon monthly mortgage payments include both principal and interest. Over time, the interest portion goes down and the principal portion goes up. – 2017-02-21

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