library(ggplot2)
library(tidyr)
library(dplyr)

# Creating the dataframe
df <- data.frame(year = 0:10, interest_rate = seq(0.05, 0.12, 0.01))

# Setting initial values
df <- df %>% mutate(balance = 30000)

# Calculating compound interest
df <- df %>% mutate(balance = balance * (1 + interest_rate) ^ year)

# Reshaping the data
df <- df %>% pivot_longer(cols = -c(year, balance), names_to = "Interest Rate", values_to = "Rate")

# Creating the line plot
plot <- ggplot(df, aes(x = year, y = balance, color = Rate)) +
  geom_line() +
  xlab("Time (years)") +
  ylab("£ (Balance)") +
  ggtitle("Compound Interest by Different Interest Rates")

# Saving the plot as a PDF
ggsave("compound_interest_plot.pdf", plot, width = 8, height = 6)