p-exp-rt.R

library(tidyverse)

# Parameters
rates <- seq(0.05, 0.20, length = 10)
time <- seq(1, 50, length = 50)
P <- 100

# Continuous compounding formula: A(t) = P * exp(r * t)
df <- expand_grid(time = time, rate = rates) |>
  mutate(value = P * exp(rate * time),
         rate = round(rate, 2) |> as.character())

# Plot
ggplot(df, aes(x = time, y = value, color = factor(rate))) +
  geom_line(size = 0.3) +
  scale_y_continuous(labels = scales::dollar_format()) +
  labs(
    title = "Growth of $100 at different interest rates",
    x = "Time (years)",
    y = "Asset value",
    color = "rate"
  ) +
  theme_minimal()