Mathematical note

Because interest and inflation are generally given as percentage increases, the formulas above are approximations.

For instance,

$i_n = i_r + p_e\,\!$

is only approximate. In reality, the relationship is

$(1 + i_n) = (1 + i_r)(1 + p_e)\,\!$

so

$i_r = \frac {1 + i_n} {1 + p_e} - 1\,\!$

The formulas in this article are exact if logarithms of index (economics)|indices are used in place of rates.

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