WebR — Juros Compostos, Perpetuidades e Anuidades

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# ============================================
# Juros Compostos, Perpetuidades e Anuidades
# Secao 18.9
# ============================================

K0 <- 1000  # capital inicial
i <- 0.12   # taxa nominal anual (12%)

cat("====== JUROS COMPOSTOS ======\n")
cat(sprintf("Capital inicial: R$ %s\n", format(K0, big.mark=".")))
cat(sprintf("Taxa nominal anual: %.0f%%\n\n", i*100))

# --- Frequencia de capitalizacao ---
cat("--- Efeito da frequencia de capitalizacao (1 ano) ---\n")
cat(sprintf("%-15s %-5s %-12s %-10s\n",
    "Frequencia", "m", "K(1)", "Taxa efet."))
cat(strrep("-", 45), "\n")
freqs <- c("Anual"=1, "Semestral"=2, "Trimestral"=4,
           "Mensal"=12, "Diaria"=365)
for (nm in names(freqs)) {
  m <- freqs[nm]
  K1 <- K0 * (1 + i/m)^m
  r_ef <- (1 + i/m)^m - 1
  cat(sprintf("%-15s %-5d %-12.2f %-10.4f\n", nm, m, K1, r_ef))
}
K_cont <- K0 * exp(i)
cat(sprintf("%-15s %-5s %-12.2f %-10.4f\n", "Continua", "inf", K_cont, exp(i)-1))

# --- Poder dos juros compostos no tempo ---
cat("\n--- Crescimento ao longo do tempo (r=12% a.a.) ---\n")
cat(sprintf("%-6s %-12s %-12s %-12s\n",
    "Anos", "Simples", "Composto", "Continuo"))
cat(strrep("-", 46), "\n")
anos <- c(1, 5, 10, 20, 30, 50)
for (t in anos) {
  simples <- K0 * (1 + i*t)
  composto <- K0 * (1 + i)^t
  continuo <- K0 * exp(i*t)
  cat(sprintf("%-6d %-12s %-12s %-12s\n", t,
      format(round(simples), big.mark="."),
      format(round(composto), big.mark="."),
      format(round(continuo), big.mark=".")))
}

# --- Perpetuidades e anuidades ---
cat("\n--- Perpetuidades e anuidades ---\n")
F <- 100  # fluxo anual
r <- 0.05
cat(sprintf("Fluxo anual: R$ %.0f  Taxa: %.0f%%\n\n", F, r*100))

VP_perp <- F / r
cat(sprintf("Perpetuidade (F/r): R$ %s\n", format(VP_perp, big.mark=".")))

for (n in c(5, 10, 20, 30, 50)) {
  VP_anuid <- F * (1 - (1+r)^(-n)) / r
  pct <- VP_anuid / VP_perp * 100
  cat(sprintf("Anuidade %2d anos: R$ %7.1f (%4.1f%% da perpetuidade)\n",
      n, VP_anuid, pct))
}

# Perpetuidade crescente
g <- 0.02
VP_cresc <- F / (r - g)
cat(sprintf("\nPerpetuidade crescente (g=%.0f%%): R$ %s\n",
    g*100, format(VP_cresc, big.mark=".")))

# --- Grafico ---
par(mfrow = c(1, 2), mar = c(4.5, 4.5, 3, 1), bg = "#f8f9fa")

# Painel 1: Juros simples vs compostos
t_seq <- 0:50
plot(t_seq, K0*(1+i)^t_seq / 1000, type = "l", lwd = 3, col = "#dc3545",
     xlab = "Anos", ylab = "Capital (R$ mil)",
     main = "Simples vs. Composto vs. Continuo",
     ylim = c(0, K0*exp(i*50)/1000))
lines(t_seq, K0*(1+i*t_seq)/1000, lwd = 3, col = "#0d6efd", lty = 2)
lines(t_seq, K0*exp(i*t_seq)/1000, lwd = 2, col = "#6f42c1", lty = 3)

legend("topleft",
       legend = c("Composto", "Simples", "Continuo"),
       col = c("#dc3545", "#0d6efd", "#6f42c1"),
       lwd = 3, lty = c(1, 2, 3), cex = 0.65, bg = "white")

# Painel 2: VP da perpetuidade vs taxa
r_seq2 <- seq(0.01, 0.15, length = 200)
VP_seq <- F / r_seq2

plot(r_seq2 * 100, VP_seq, type = "l", lwd = 3, col = "#0d6efd",
     xlab = "Taxa de juros (%)", ylab = "VP (R$)",
     main = "Perpetuidade: VP = F/r",
     ylim = c(0, 12000))

# Marcar pontos
r_marks <- c(0.02, 0.05, 0.10)
VP_marks <- F / r_marks
points(r_marks*100, VP_marks, pch = 19, col = "#dc3545", cex = 1.5)
for (k in seq_along(r_marks)) {
  text(r_marks[k]*100 + 0.8, VP_marks[k],
       format(round(VP_marks[k]), big.mark="."),
       col = "#dc3545", cex = 0.7, font = 2, pos = 4)
}

text(8, 8000, "Queda de r\nduplica o VP!",
     col = "#6f42c1", cex = 0.8, font = 2)

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