Seigniorage: Based on the paper: Maurice Obstfeld, 'Notes on Seigniorage and Budget Constraints' (Berkeley University, Economics 202A, Fall 2012) 1, SE = m_t = m_t-1 + (inflation)m_t-1.

But when I calculate it from SE=(M_t-M_t-1)/P_t , I hit SE= M_t/P_t - M_t-1/P_t-1 + [(P_t - P_t-1 )/P_t-1] X (M_t-1/P_t).

Doesn't the last part have to be M_t-1/P_t-1 instead of M_t-1/P_t to be able to convert it to m_t-1 ?

Please show me the workings of how seigniorage can be calculated as the real money holdings times inflation tax.