Esercizi di Matematica finanziaria

Esercizi sui regimi

Es. 1 esame 030614 sez.

i_t = 0,08

1. U(t) = (1+i) = (1+i_tℓ_k)^k →

   i = (1+i_tk)^1/k-1

   i = (1+0,08)²-1 = 0,1664 (16,64%)

2. d_1/4 inv

   d_1/4 = 0,08

   d_1/4 = 0,0474; 7,4074%

3. d_1/4 → d_1/12

   i_ik = t_k

   i_ik = (1+i)^1/8-1

   i_d = (1+0,1664)^1/4-1 = 0,03823

   d_1/4 = 0,03823/ (1+0,03823) = 0,03725; 3,725%

4. b 5_1/4 (1/4) = 0,15622 = -15,6822%

5. d = ln(1-dρ) ρ ρ

   ρ = ln(1-d) = ln(1-0,12667) = 0,153822 = 15,3822%

Es. 1 esame 100215

1. t_{k x}

   i =

2. w 1+i

   i =

d) r₂ = ln(1.033158) = 2.83872

V = 4t i = 0.2

a) i_1/4 = 4i_t i_1/4 = i_0.2 1.02 - 1 = 0.02

b) i = 0.02 0.02: 4 = 0.005

c) i₄ = 4

γ₄ = 5.1

d) ? V(t) = (1+i)t

e) ? V(t) = (1+i)⁴

T₄ = τ i₄ = 0.025

i = K₄ 1_i1/4 = 4 ψ 0.02

T₅ = 1 0 10 11

J₄ =10 0

d) d₂ ? V(t) = ¹⁄_1+it

J_1/4 K_i = 0.20

τi + i = ι _i = <2 - 0.40

b) S_1/4 = ^i_1/4⁄_1/4 i_1/4 = ^ι+i⁄⁄^1/4 = ^0.20⁄₄ = 0.05

d) i_1/4 = 0.05

e) d_tt 1.d.sub_1/4 K_it ^0.047698 4 = 0.8576

K = 1.05¹⁄<1 = 0.215506

i₂ = (1+i)²⁄⁴ = 0.47745

b) i = ¹⁺ⁱ = 0.47745

τ₂ = ^0.47745.

d₃ = d₁ de d_u.c = 0,0133

d_{r1c = d0,08}

d₁₂ = 0,08 i₁ = 0,04

Es 2 esame 2\0114

D = 300 K = 2000 tre anni

1. i?

d₃ = 300 = 0,15

2000

i₃ = 0,15 = 0,17647

0,85

i = i_1ike K = 0,17647 x 1 = 0,058823

2. i₃ = 0,17647

i = (1+i_i3K – 1

i = (1,47647)^1/3 - 1 = 0,05566

3. c)

d₃ = 0,15

d = d₃ x 1 = 0,05

3

i = 0,05 = 0,052632

0,85

4. d) C = 8000

T_{i1d,2m e 15g N 7 conto commerciale}

T_c 360 + 60 15 = 435

360 360 360

i = 0,052632

i₄₃₅ ? d = 0,05 435 = 0,06402

360

d₄₃₅ 360

0,06402 = 0,064305

0,934589

N = C (1+i₄₃₅) = 8000 + 514,44 = 8514,44

360

Es. 1 esame 210114

1. 4₁₂ 4 4 4 4 4 23 29

2. √5 : √81 : √4 : 23 ...

   • 4 4 4 1
   • 15 16 17 ... 44

3. 3₆ : 2₆ : 1 : 6₆

4. 2₁₀ : 2₁₁ : 2₃₀

Es. 2 esame 230614

• b) ^{1 - 1,0842} / _0,03 = ^{1 - √42} / ₁₁₂ = ^{d - √n} /_d

• 1,08, 1,08⁴², d - √n

• 0 1 1 1 0

  • 1 2 3 ... 42
  • ... 41 42
  • 0,8 2 4 3 ... 42
  • q - 4 4 4 4

• 1,08¹⁵ 1,03⁴², √nⁿ, d^{1 - √n}

• 0,03 0,8 0,8

• i,0

• 0 - 15 16 17 ... 58

• 1,08⁷, 1,03⁴², √nⁿ, d^{1 - √n},

• 15 16 17 ... 56 57

• e) ^1,0837 / _1,03√2 = ^{1 - √n} / ₁₁₄

• (1+i)¹⁴ = 1₁₄

• 0,03 0,8 0,8

Es. 5 esame 250208

1. 25/2/08 20 rate semestrali, costanti R

2. d) prima rata il 25/2/08 V = R · a_2n V = R : 0 _20∕112 = R · 1 - ^√20 /_√20

3. b) ultima rata il 25/2/08 V = R · a_2n = V : 20∕_{1 12} = R · 1 - ^√20 /_√n ~ R : 5 a_n - ^√20 /_√n

4. c) ultima rata il 25/2/08 Π = R · 5 a_n , u^s = R · 20∕1 , (1+i)^s /_{1 12}

Es. 6 esame 111208

D = 5000 5 rate mensili i_1/12 = 8% , amm. italiano

i = (1,08)^1/12 - 1 = 0,0259712

i_1/12 = (1,0259712) - 1 = 0,018426

d_1/12 = 0,018426 - 0,018056

1,018426 /

• 0 - R_c 95,28 C_c 0 I_c 95,28 D_c 5000
• 1 - 1076,22 1000 76,22 4000
• 2 - 1052,17 1000 57,17 3000
• 3 - 1038,11 1000 38,11 2000
• 4 - 1019,06 1000 19,06 1000
• 5 - 1000 1000 0 0

Es. 4 esame 170112

D = 5000 5 rate semestrali, i = 5% , amm. tedesco

i_1/2 = (1,05)^1/2 - 1 = 0,024695

d_1/2 = 0,024695 = 0,024699

1,024695

R = v ⋅ D - 1D = /

ann. fin. trim. fin. 1 ^{1 i ⋅ D} _

_ _ (_ _ 5

_ _ _ _ _ _

1,024695 1234,75 = 0,8578 1052,9 =

= 10493,80

• h - R_c C_c I_c D_c
• 0 - 1204,85 0 1204,85 5000
• 1 - 10493,80 8518,22 975,58 4682,08
• 2 - 10493,80 8933,27 740,53 32228,32
• 3 - 10493,80 8984,11 489,69 20734,71
• 4 - 10493,80 10240,91 252,89 10493,80
• 5 - 10493,80 10493,80 0 0

Esercizi su ammortamenti

Es. 4 esame 060212

I₀ = iD₀ i_e = I_t

D_iniz = 2700

Es. 5 esame 060212

D₀ = (n-k)_e C

I_e = dD_e = d(n-k)_e C

R₁ - C₁ I₁

R₁₀ = C + I₁₀ C + d(n-10)_e C = C + d(n-10)_e C = C + d(n-10) C= C + d(n-10 C) R_n = C + I_ne C + d(n-1)_e C = C + d(n-1)_e C = C + d(n-11)C

R₁₀-R_n = -10 Cd + 11Cd

R₁₀-R_n = Cd

d = R₁₀ - R_n = 11882,72 - 11450,62 - 0,0740874 5833,33

i = I_e = dR

i - 0,0740874

i - 0,08