formulas_2_2020_novo

Prévia do material em texto

2ª FOLHA DE FÓRMULAS – Matemática Financeira/UPF – Profa. Rosana Maria Luvezute Kripka 
 
𝑀 = 𝐶 (1 +
𝑖
𝑘
)
𝑘×𝑛
 (1 + 𝑖𝑒)
1 = (1 +
𝑖
𝑘
)
𝑘
 𝑖𝑒 = (1 +
𝑖
𝑘
)
𝑘
− 1 𝑀 = 𝐶(1 + 𝑖𝑒)
𝑛 
 
𝑗 =
𝑃𝑡
𝑃0
− 1 =
𝛥𝑃
𝑃0
 𝑖𝐴𝐶 = (1 + 𝑖1)(1 + 𝑖2) … (1 + 𝑖𝑛) − 1 𝑀 = 𝐶(1 + 𝑖𝐴𝐶) 𝑀 = 𝐶𝑒
𝑖.𝑛 
 
𝑀 = 𝐶(1 + 𝑖1)(1 + 𝑖2) … (1 + 𝑖𝑛) 𝐷𝑟 = 𝑁 − 𝐴 𝐴 = 𝑁(1 + 𝑖)
−𝑛 𝐴 =
𝑁
(1 + 𝑖)𝑛
 
 
𝑀1 = 𝐶(1 + 𝑖) 𝑀2 = 𝐶(1 + 𝑗) 𝑀1 = 𝐶(1 + 𝑗)(1 + 𝑟) 𝑟 =
(1 + 𝑖)
(1 + 𝑗)
− 1 
 𝑉 = 𝑅0 +
𝑅1
(1 + 𝑖)
+
𝑅2
(1 + 𝑖)2
+ ⋯ +
𝑅𝑛
(1 + 𝑖)𝑛
 
 
𝑎𝑛¬ 𝑖 = [
(1 − (1 + 𝑖)−𝑛)
𝑖
] 𝑉 = 𝑅 ⋅ 𝑎𝑛¬ 𝑖 𝑉 = 𝑅 ⋅ [
(1 − (1 + 𝑖)−𝑛)
𝑖
] 
 
𝑛 =
− 𝑙𝑜𝑔 [1 − (
𝑉 ⋅ 𝑖
𝑅 )
]
𝑙𝑜𝑔(1 + 𝑖)
 𝑉 = 𝑅 ⋅ (1 + 𝑖) ⋅ 𝑎𝑛¬ 𝑖 𝑉 = 𝑅 ⋅ (1 + 𝑖) ⋅ [
(1 − (1 + 𝑖)−𝑛)
𝑖
] 
 
𝑛 =
− 𝑙𝑜𝑔 {1 − [
𝑉 ⋅ 𝑖
(𝑅 ⋅ (1 + 𝑖))
]}
𝑙𝑜𝑔(1 + 𝑖)
 𝑅 = 𝑉 ⋅ (𝑎𝑛¬ 𝑖)
−1 𝑅 = 𝑉 ⋅ [
(1 − (1 + 𝑖)−𝑛)
𝑖
]
−1
 
 
𝑅 = 𝑉 ⋅ [(1 + 𝑖) ⋅ 𝑎𝑛 ¬ i]
−1 𝑅 = 𝑉 ⋅ {(1 + 𝑖) ⋅ [
(1 − (1 + 𝑖)−𝑛)
𝑖
]}
−1
 
 
𝑆𝑛¬𝑖 =
[(1 + 𝑖)𝑛 − 1]
𝑖
 𝑀′ = 𝑅 ⋅ (1 + 𝑖) ⋅ 𝑆𝑛¬𝑖 𝑅 = 𝑀
′ ⋅ [(1 + 𝑖) ⋅ 𝑆𝑛¬𝑖]
−1 
 
𝑛 =
𝑙𝑜𝑔 [
𝑀′ ⋅ 𝑖
(𝑅 ⋅ (1 + 𝑖))
+ 1]
𝑙𝑜𝑔(1 + 𝑖)
 𝑀′ = 𝑅 ⋅ 𝑆𝑛¬𝑖 𝑅 = 𝑀
′ ⋅ (𝑆𝑛¬𝑖)
−1 𝑛 =
𝑙𝑜𝑔 [
𝑀′ ⋅ 𝑖
𝑅
+ 1]
𝑙𝑜𝑔(1 + 𝑖)