• Zinseszins Zinsfaktor
  • Deliah Herbstritt
  • 21.07.2020
  • Mathematik
  • Zinsen
  • E
  • 8
  • Einzelarbeit
  • Arbeitsblatt
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1
Der Zinsfaktor q = 1 + p%
Berechne den Zinsfaktor q.

Zinssatz p%

4%

3,5%

10%

7%

5,5%

Zinsfaktor q

q = 1,04

q = 1,035

q = 1,1

q = 1,07

q = 1,055

2
Der Zinsfaktor q = 1 + p%
Fülle die Tabelle aus.

Zinssatz p%

20%

6,5%

2%

15%

0,3%

Zinsfaktor q

1,2

1,065

1,02

1,15

1,003

3
Berechne jeweils das Kapital nach einem Jahr, nach zwei und nach drei Jahren.
  • Gegeben: Kapital K0\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K^0 = 250,00€, p = 5%
    Gesucht: K1\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_1, K2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_2, K3\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_3
  • Gegeben: Kapital K0\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K^0 = 1 200,00€, p = 4%
    Gesucht: K1\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_1, K2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_2, K3\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_3
  • Gegeben: Kapital K0\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K^0 = 4 600,00€, p = 2,7%
    Gesucht: K1\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_1, K2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_2, K3\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_3
Lösung3
a)
q=1+p%\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} q=1+p\%
q=1+5%\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} q= 1+5\%
q=1,05\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} q= 1{,}05

b)
q=1+p%\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} q=1+p\%
q=1+4%\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} q= 1+4\%
q=1,04\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} q= 1{,}04

a)
q=1+p%\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} q=1+p\%
q=1+2,7%\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} q= 1+2{,}7\%
q=1,027\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} q= 1{,}027


K1=250,001,05=262,50\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_1=250{,}00€\cdot1{,}05 = 262{,}50€
K2=262,501,05275,63\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_2=262{,}50€\cdot1{,}05 \approx 275{,}63€
K3=275,631,05289,41\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_3=275{,}63€\cdot1{,}05 \approx 289{,}41€

K1=1200,001,04=1248,00\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_1=1200{,}00€\cdot1{,}04 = 1248{,}00€
K2=1248,001,04=1297,92\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_2=1248{,}00€\cdot1{,}04 = 1297{,}92€
K3=1297,921,041349,84\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_3=1297{,}92€\cdot1{,}04 \approx 1349{,}84€

K1=4600,001,027=4724,20\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_1=4600{,}00€\cdot1{,}027 = 4724{,}20€
K2=4724,201,0274851,75\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_2=4724{,}20€\cdot1{,}027 \approx 4851{,}75€
K3=4851,751,0274982,75\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} K_3=4851{,}75€\cdot1{,}027 \approx 4982{,}75€