FIN1020 TN1

Travail  noté 1

Question 1

a)

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PMT : ?

i : 7%

b) PV = PMT(1- (1 + i)*-n/i) + PMT(1 - (1 + i)*-n/I)  (1 + i)*-n

35 000 ((1 – (1.07)*10/0.07) + 40 000((1 – (1.07)*10/0.07) (1.07)*-10

PV= 245 825.35$ + 142 817.31$

PV = 388 642.66$

Pour retirer 35 000$ pendant 10 ans et 40 000$ pendant 10 ans, mon cousin doit avoir 388 642.66$

c)

PMT = ?

PV = 388 642.66$

I = 7%

N = 40

388 642.66$ = PMT(1 - (1 + 0.07)-40)/0.07

PMT = 6648$

Mon cousin devra verser 6648$ annuellement.

d) 0.5% x 12 = 6% (taux capitalisé mensuellement)

(1 + 6%)*12/12 – 1 = 6.17%

35 000 ((1 – (1.0617)*10/0.0617) + 40 000((1 – (1.0617)*10/0.0617) (1.0617)*-10

255 540.91 + 164 484.91

Avec un taux de rendement de 0.5%, mon cousin devra accumuler 416 025.83$

Question 2

a)

PV : 300 000 – 40 000 = 260 000$ pour la mise de fond

N = 240 périodes

I = ?

(1 + i)2  = (1 + i)12

(1 + 0.08/2)2 = (1 + I)12

(1.04)2/12 – 1 = i

I = 0.06558%

1 + i-n - 1

1 + 0.006558-240

PMT = 2153.73$

b)

21.53.69$ X 240 = 516 885.60$

516 885.76 – 260 000 = 256 885.60$

c)

(1 + i)26 = (1 + i)2

(1 + i)26/26 = (1 + 0.04)2/26

I = (1.04)1/13 – 1

I = 0.3022%

N = 26 x 20 = 520

1 + 0.0322 -520 – 1

PMT = 992.37$

d)

PMT = 2153.69$

N = 240 – 12 = 228

(1 + i)-n - 1

I = 0.006558-228 – 1

PV = 2153.69

Solde restant après 12 mois : 254 418.02$

260 000 – 254 418.02 = 5581.98$

12 x 2153.69 = 25 844.28$

Total des intérêts payés après 12 mois : 25 844.28 – 5581.98 = 20 262.30$

e)

(1 + i)2 = (1 + i)12

(1 + 0.095/2)2 = (1 + i)12

(1.0475)2/12 – 1 = i

I = 0.007764 = 0.7764%

PMT = ?

I = 0.7764%

N = 240 – 12 = 228

1 + 0.007764-228 – 1

PV = 254 418.02$

PMT = 2384.10$

f)

(1 + i)1 = (1 + i)6

(1 + 0.03)1 = (1 + i)6

(1.03)1/6 – 1 = i

I = 0.004939 = 0.4939%

N = 240

1 + i -n -1

1 + 0.004939-240 – 1

PMT = 1851.76$

Question 3

a)

PV = FV (1+ i)-n (1+i)-n  

PV = 50 000 (1+012/12)-12x2 (1+0.08/4)-4x2
PV = 50 000 (1.01)-24 (1.02)-6
PV = 50 000 (0.787566)(0.853490)

PV = 33 609 $

b)

FV= PMT (1 + i)n / i * (1 + i)n + PMT (1+i)n -1/i

i = 8%

(1 + I1/m1) m1 = (1 + I2/m2)m2

 (1 + 8%/4)4= (1 + i)12

I = 0.006623 ou 0, 6623 %

FV= PMT (1+12%/12)24-1 /0.01 * (1+8%/4)8 + PMT (1+0.00623)24-1/0.00623)

50 000 = PMT 26,973465 X 1,171659 + PMT 25,800672

50 000 = PMT 57.404375

PMT= 871$

c)

 (1 + i1/m1) m1= (1 + i2/m2) m2

(1 + 0.12/12)12 =  (1 + i) 4

I = 0.03

FV  = PMT (1 + i)8 -1 / 0.03  X (1 + 0.08/4 )8 + (1 + 0.08/4)8-1/ 0.08/4

50 000 = PMT 10,418786 + PMT 8,5822969

PMT = 2631$ trimestriellement

Question 4

a)

P0 = ?

N 10 ans ⟹  n =20 périodes

VN= 1000$

IC = 11.5% / 2 = 5.75%