(1)Matematyka finansowa - wzory na sprawdzian i egzamin Na sprawdzian

Matematyka finansowa - wzory na sprawdzian i egzamin Na sprawdzian:

¯

r = _m^r; K_N = K₀(1 + N r); K_N = K₀(1 + r)^N; K_t = Ke^rt; r_ef = (1 + r)^m− 1; r_ef = ln(1 + r);

r_ef = e^r − 1; r = (1 − p)r; 1 + R = (1 + r₁)ⁿ¹(1 + r₂)ⁿ² · . . . · (1 + r_p)^np; r_prz = p(1 + r^N ₁)ⁿ¹(1 + r₂)ⁿ² · . . . · (1 + r_p)^np − 1; K_re,t = _1+i^Kt

C; (1 + r_re)(1 + i) = (1 + r); r_re = ^r−i_1+i; K = K0(1 + wi); ic = (1 + i1)ⁿ¹(1 + i2)ⁿ² · . . . · (1 + ip)^np − 1; iprz = ^N√

1 + ic − 1;

iprz = ^Np(1 + i₁)ⁿ¹(1 + i2)ⁿ²· . . . · (1 + ip)^np− 1; KN = K(1 + r)^N. Dodatkowo na egzamin:

N P V (r) = PN

j=0C_j(1 + r)^−tj; N P V (r^∗) = 0; D = _P¹ PN

j=1t_jC_j(1 + r^∗)^−tj; S_k = W^q_q−1^k−1; S_k= W q^q_q−1^k−1; S_k = R^q_q−1^k−1; S_k = Rq^q_q−1^k−1; P V = S_Nq^−N; R_w = Kr; R_w = ^Kr_q ; S_k =

(R^qk_q−a^−ak, q 6= a;

kRq^k−1, q = a. ;

S_k =

(Rq^qk_q−a^−ak, q 6= a;

kRq^k, q = a. ; Kq^N = S_N; K_N = Kq^N − S_N; K_m = PN

j=m+1R_jq^m−j = Kq^m − Pm

j=1R_jq^m−j; K_N = 0; R_m = U_m + I_m; I_m = K_m−1r;

U_m = K_m−1 − K_m; K_m = K_m−1 − U_m; PN

j=1U_j = K; K_m = K − Pm j=1U_j; R = Kq^{N q−1}_qN−1; K_m = Kq^m− R^q_q−1^m−1; U = ^K_N; K_m = K − mU ; W_akt = W_nom− D_H = W_nom(1 − dn);

r = _1−dn^d ; d = _1+nr^r ; P = W_nom(1 + r^∗)^−N; W_k = W_nomm^r; P = W_k^1−(q_q∗^∗−1^)−N + W_nom(q^∗)^−N; P = ^W_r∗^k; 1 + ^{Y T M}_m
m

− 1 = IRR; P = PN

j=1D_j(1 + r^∗)^−j + P_t(1 + r^∗)^−t; P = P∞

j=1D_j(1 + r^∗)^−j; P = _r^D∗; P = ^D_r⁰∗^(1+g)−g ; P = ^D_r⁰∗^(1+g−g₁¹⁾1 − ^1+g_1+r∗¹

n1

 +^D_(r^0(1+g∗−g₂¹)(1+r^)n1(1+g∗)ⁿ¹²⁾.