nach einem Monat K = Ko*(1+p/12) - R
nach 2 Monaten K = (Ko*(1+p/12) - R )(1+p/12) - R ) = Ko*(1+p/12) ^2 - R*(1+p/12) - R
nach 3 Monaten K= (Ko*(1+p/12) ^2 - R*(1+p/12) - R ) (1+p/12) - R
= Ko*(1+p/12) ^3 - R(1+p/12) ^2 - R*(1+p/12) - R
etc also K1 = Ko(1+p/12) ^12 - R*( (1+p/12) ^11 + R*(1+p/12)^10 +......+1 )
mit geom Reihe:
K1 = Ko(1+p/12) ^12 - R * (1+p/12) ^12 - 1 ) / (p/12)
= Ko(1+p/12) ^12 - 12*R * (1+p/12) ^12 - 1 )