MATEMATYKA FINANSOWA WZORY
Kt =� K0 �� (1+� r ��t) , O =� K0 �� r ��t , r(t) =� r ��t Kn =� K0 �� (1+� r1 �� n1 +� r2 �� n2 +� ... +� rp �� np )
n1r1 +� n2r2 +�L�+� nprp
Z1n1r1 +� Z2n2r2 +�K�+� Zk nk rk
r =� , rSR =� Kn =� K0 (1+� r)n , O =� K0 [(1+� r)n -�1] ,
n1 +� n2 +�L�+� np Z1n1 +� Z2n2 +�K�+� Zk nk
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��ć� r ��n��m ł�
r
p
1 2
r(n) =� (1+� r)n -�1 Kn =� K0 ć�1+� �� O =� K0 ę� 1+� -�1ś� Kn =� K0 (1+� r1)n (1+� r2 )n L��� (1+� rp )n
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m
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ę�Ł� m ł� ś�
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m
n��m
r
ć�1+� ��
r
ć�1+� ��
n
p
1 2
ref =� -�1 Kn =� K0en��r
r(t) =� -�1 r =� (1+� r1)n (1+� r2 )n L��� (1+� rp )n -� 1, �� ��
�� ��
m
m
Ł� ł� Ł� ł�
n(�n +�1)� n(�n -�1)�
��n ł� ��n ł�
g d
Kt =� K0 �� (1+� r)[�t]� �� (1+� r �� (t)) Kn =� K �� +� r Kn =� K �� +� r
ę� ś� ę� ś�
2m 2m
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r
1+�
ć�ć� r ��n��m ��
1+� r r K �� er ��(�en��r -�1)�
g
g g m
����1+� �� -�1�� g d
Kn =� K �� ��(�(1+� r)n -�1)� Kn =� K �� �� Kn =� Kn ć�1+� �� Kn =�
�� ��
��Ł� m ł� ��
r
r m er -�1
Ł� ł�
Ł� ł�
m
n��m
ć� ��
1 1 r K ��(�en��r -�1)� K0 =� K0 �� er
��
d d d g d
Kn =� K �� ��(�(1+� r)n -�1)� Kn =� K �� ����ć�1+� -�1�� Kn =�
���� m �� ��
r
r er -�1
Ł�Ł� ł� ł�
m
-�nm
r
K0 =� Kn (1+� r n)-�1 , K0 =� Kn (1+� r)-�n , K0 =� Kn ć�1+� �� K0 =� Kne-�r��n
�� ��
m
Ł� ł�
1+� r 1
n
K �� ��(�(1+� r)n -�1)� K �� ��(�(�1+� r)� -�1)� -�n
1+� r 1-�(�1+� r)�
g r d
r
K0 =� =� K �� ��[�1-� (1+� r)-�n]� K0 =� =� K ��
n
(1+� r)n r r
(�1+� r)�
-�n��m
r
ć�1+� ��
r
1-�
-�n��m
1+�
��ł�
r r
m
ć�1+� ��K0 =� K �� �� ��
g d g d Ł� ł� g d
m
K0 =� K0 (�1+� r)� K0 =� K �� �� K0 =� K0 ć�1+� ��
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ę�1-� �� �� ś�
r r
m m
Ł� ł� Ł� ł�
��
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m m
K �� er ��(�en��r -�1)�e =� K �� er ��(�1-� e-�n��r )� K0 =� K ��(�en��r -�1)�e =� K ��(�1-� e-�n��r )� K0 =� K0 �� er
g -�n��r d -�n��r g d
K0 =�
er -�1 er -�1 er -�1 er -�1
m
ref -� i
ó� ó� ó�
r =� r =� r +� i +� r ��i i =� (�1+� i )� -� 1 =� (�1+� i1)���(�1+� i2 )���...��(�1+� im )�-�1
�� j
1+� i
j=�1
m
m
i =� m (�1+� i )� -� 1 =� (�1+� i1)���(�1+� i2 )���...��(�1+� im )� -�1
�� j
j=�1
r
D =� Kn -� K0 , DH =�Kn �� d �� n D =� DH d =� .
1+� r �� n
S
S
n
T1 =� T2 =� ... =� TN =� T , An =� T +� On T =� Sn =� S �� (1-� ) , On =� r �� Sn-�1 , An =� ��(�1+� (N -� n +�1) �� r)�;
N
N
N
q -�1 r
A1 =� A2 =� ... =� AN =� A, A =� Tn +� On , A =� S �� qN �� q =�1+�
m
qN -�1
p
1 2
Kn =� Kn (1+� r1)n (1+� r2 )n L��� (1+� rp )n
Kn
-�1
ć� ��
Kn K0
��n��m Kn -�1�� �� m
ref =� er -�1
n
Kn =� K0 (1+� ref )n ref =� -�1 Kn =� K0 (1+� n �� r) r =� =� r =�
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K0 n K0 ��
Ł� ł�
1
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