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BAL 0 = PV ( INT 1 = 0 und PRN 1 = PMT zu Beginn des Tilgungszeitraumes)
u Interne Umrechnung der Zinssätze (zwischen Nominalzins und Effektivzins)
Der Nominalzinssatz (der dem Anwender eingegebene I %-Wert, Jahreszinssatz) wird in den
effektiven Zinssatz ( I % ' ) einer Ratenperiode (Effektivzins) umgerechnet, wenn die Anzahl der
jährlichen Ratenzahlungen von der Anzahl der Zinsberechnungsperioden abweicht.
Nach der Umrechnung des Nominalzinssatzes in den internen relativen Zinssatz wird die
folgende Darstellung für i dann auch in allen weiteren Berechnungen genutzt.
Drücken Sie 4(AMT) im Display Finanzmathematik 1, um das Eingabefenster für die
Tilgungsberechnungen zu öffnen.
4(AMT)
PM1 ....... Index1, erster Betrachtungszeitpunkt zwischen 1 und n
PM2 ....... Index1, zweiter Betrachtungszeitpunkt zwischen 1 und n
n ........... Raten
I % ......... Zinssatz
PV ........ Gesamtdarlehen (Anfangskapital, Gesamtschuld)
PMT ..... Rate (Ratenzahlbetrag)
FV ........ Restschuld nach der Schlussrate (Endkapital)
P / Y ....... Anzahl der Ratenzahlungen pro Jahr
C / Y ....... Anzahl der Verzinsungsperioden pro Jahr
a : INT
PM1
= I BAL
PM1–1
× i I × (PMT sign)
b : PRN
PM1
= PMT + BAL
PM1–1
× i
c : BAL
PM2
= BAL
PM2–1
+ PRN
PM2
d :
Σ
PRN = PRN
PM1
+ PRN
PM1+1
+ … + PRN
PM2
e :
Σ
INT = INT
PM1
+ INT
PM1+1
+ … + INT
PM2
PM2
PM1
PM2
PM1
a : INT
PM1
= I BAL
PM1–1
× i I × (PMT sign)
b : PRN
PM1
= PMT + BAL
PM1–1
× i
c : BAL
PM2
= BAL
PM2–1
+ PRN
PM2
d :
Σ
PRN = PRN
PM1
+ PRN
PM1+1
+ … + PRN
PM2
e :
Σ
INT = INT
PM1
+ INT
PM1+1
+ … + INT
PM2
PM2
PM1
PM2
PM1
I
%' =
I%
(1+ ) –1
[C/Y ]
[P/Y ]
{ }
×
100
100 × [C/Y ]
I
%' =
I%
(1+ ) –1
[C/Y ]
[P/Y ]
{ }
×
100
100 × [C/Y ]
i = I%'÷100 i = I%'÷100
7-5-2
Tilgungsberechnungen (Amortisation)
193


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