n
q p = nq 0,3
12 · 0,3% = 3,6% 4,8
4,8%
= 0,8%
6
12%
= 1% (1 + 0,01)12 H" 12,68%
12
p pe n
t Kt t
n

n
p p p p
100 100 100 100
K1 = 1 + 1 + · · · 1 + = 1 +
n n n n
t·n
p
100
Kt = K0 1 +
n
n
p
100
pe = 100 1 + - 1
n
n
n n"
x
1 + - ex
--
n
p
100
K1 = K0e
p
100
Kt = K0et

p
100
pe = 100 e - 1
 10 000
K0 = 10 000 p = 6
n = 12
24
6
K2 = 10 000 1 + = 11 271,60
100 · 12
1 271,61
n = 1
2
6
K2 = 10 000 1 + = 11 236
100
1 236,00

12
24
pe = 100 1 + - 1 = 26,82
12 · 100

2
25
pe = 100 1 + - 1 = 26,56
2 · 100
K
b
p
p
q =
1200
q = p/5200
 Ki
i i
q qKi-1
b Ki = Ki-1 + qKi-1 - b
K0 = K
K1 = K(1 + q) - b

K2 = K(1 + q) - b (1 + q) - b = K(1 + q)2 - b((1 + q) + 1)


K3 = K(1 + q) - b (1 + q) - b (1 + q) - b = K(1 + q)2 - b((1 + q)2 + (1 + q) + 1)

Kn = K(1 + q)n - b (1 + q)n-1 + (1 + q)n-2 + · · · + (1 + q)2 + (1 + q) + 1
n

(1 + q)n - 1 1
Kn = K(1 + q)n - b = b - (b - Kq) (1 + q)n
q q
b > Kq
n b Kn = 0
Kn b
q(1 + q)n
b = K
(1 + q)n - 1
b > Kq n Kn
q
1/q
b
(1 + q)n =
b - Kq

b
ln [(1 + q)n] = ln
b - Kq
n ln(1 + q) = ln b - ln(b - Kq)
ln b - ln(b - Kq)
n =
ln(1 + q)

ln b - ln(b - Kq)
n = ,
ln(1 + q)
x x
150 000
6
1 000 1 150
6
q = = 0,005 K = 150 000
1200
n = 20 · 12 = 240
0,005 · (1,005)240
b = 150 000 = 1 074,65
(1,005)240 - 1
Kq = 750 b = 1 000

ln 1 000 - ln(1 000 - 750)
n = = 277,95 = 278 .
ln 1,005
b = 1 150

ln 1 150 - ln(1 150 - 750)
n = = 211,74 = 212 .
ln 1,005
i
qKi-1 bi
K
qKi-1
n
K
bi = qKi-1 +
n
K K
Ki = Ki-1 + qKi-1 - bi = Ki-1 + qKi-1 - qKi-1 - = Ki-1 - .
n n

i i
Ki-1 = K - K = K 1 -
n n

K i - 1 1
bi = qKi-1 + = K q 1 - +
n n n
 n
b

1 K
b = b1 = K q + Ò! n =
n b - qK
i = 121
1 074,65
1 000
1 150
n = 240 K/n = 625
i = 1, 240, 121

1
b1 = 150 000 0, 005 + = 1 375
240

0,005 1
b240 = 150 000 + = 628,13
240 240

120 1
b121 = 150 000 0,005 1 - + = 1 000 .
240 240
1 375 628,13 1 000
b = 1 075,65
b


1 b 1 1 1 074,65 1
i = n 1 - - + 1 = 240 1 - - + 1 = 87,112
q K n 0, 005 150 000 240
1 075 1 071,88
1 000 b - Kq = 250
1 150 b - Kq = 400
1 000 n = 600
1 150 n = 375
251,25 402