2 Finanzmathematik-Schüler

21
jährlich Rentenbarwert Rentenendwert
vorschüssig
n
n
0
q
1
1
q
1
q
q
r
R ⋅
−
−
⋅
⋅
=
)
1
q
(
q
)
1
q
(
q
R
r n
n
0
−
⋅
−
⋅
⋅
=
q
log
1
q
r
)
1
q
(
R
1
log
n
0
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
+
⋅
−
⋅
−
=
1
q
1
q
q
r
R
n
n
−
−
⋅
⋅
=
)
1
q
(
q
)
1
q
(
R
r n
n
−
⋅
−
⋅
=
q
log
1
q
r
)
1
q
(
R
log
n
n
⎥
⎦
⎤
⎢
⎣
⎡
+
⋅
−
⋅
=
nachschüssig
n
n
0
q
1
1
q
1
q
r
R ⋅
−
−
⋅
=
)
1
q
(
)
1
q
(
q
R
r n
n
0
−
−
⋅
⋅
=
q
log
1
r
)
1
q
(
R
1
log
n
0 ⎥ ⎥⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
+
−
⋅
−
=
1
q
1
q
r
R
n
n
−
−
⋅
=
)
1
q
(
)
1
q
(
R
r n
n
−
−
⋅
=
q
log
1
r
)
1
q
(
R
log
n
n
⎥
⎦
⎤
⎢
⎣
⎡
+
−
⋅
=
- vorschüssige, jahreskonforme Ersatzrente:
⎥
⎦
⎤
⎢
⎣
⎡
+
⋅
+
⋅
= )
1
m
(
2
100
/
p
m
r
r e
- nachschüssige, jahreskonforme Ersatzrente:
⎥
⎦
⎤
⎢
⎣
⎡
−
⋅
+
⋅
= )
1
m
(
2
100
/
p
m
r
r e
- vorschüssiger, unterjähriger Rentenbarwert: m
n
.
rel
.
rel
m
n
.
rel
.
rel
0
q
1
1
q
1
q
q
r
R ⋅
⋅
⋅
−
−
⋅
⋅
=
- nachschüssiger, unterjähriger Rentenendwert:
1
q
1
q
r
R
.
rel
m
n
.
rel
n
−
−
⋅
=
⋅