Illustrating compound growth using absolute investment value, change from initial investment, and percentage change from initial investment.

compounding.R

############################################################
#                                                          #
#         The effect of starting investment amount         #
#      on returns realised. The magic of compounding       #
#                                                          #
############################################################

# Load packages
library(ggplot2)

# Define compounding function (return a vector of length: period_of_investment)
compounder <- function(initial_investment = 1000,
                       period_of_investment = 30,
                       annual_growth = 0.05) {

    # Create a list the length of the investment period
    period <- vector(mode = 'list',
                  length = period_of_investment)

    # Set the initial_investment amount as the first value of period
    period[[1]] <- initial_investment

    # Compound the initial investment over the investment period
    # by a constant rate of annual growth
    for(i in 2:length(period)) {
        period[[i]] <- period[[i - 1]] + (annual_growth * period[[i - 1]])
    }

    # Return
    unlist(period)
}

# Generate a vector of compound growth over 30 years for a:
## i) large initial investment and a constant annual growth rate of 2.5%
large_2.5p <- compounder(initial_investment = 70000,
                         period_of_investment = 30,
                         annual_growth = 0.025)

## ii) small initial investment and a constant annual growth rate of 2.5%
small_2.5p <- compounder(initial_investment = 7000,
                         period_of_investment = 30,
                         annual_growth = 0.025)

## iii) small initial investment and a constant annual growth rate of 5.0%
small_5.0p <- compounder(initial_investment = 7000,
                         period_of_investment = 30,
                         annual_growth = 0.05)

# Make a dataframe (long format)
df <- data.frame(period = rep(1:30, 3),
                 investment = c(rep('large (2.5% growth)', 30),
                                rep('small (2.5% growth)', 30),
                                rep('small (5.0% growth)', 30)),
                 value = c(large_2.5p, small_2.5p, small_5.0p),
                 starting_value = c(rep(70000, 30),
                                    rep(7000, 30),
                                    rep(7000, 30)))

# Plot the raw data
ggplot(data = df) +
    aes(x = period,
        y = value,
        colour = investment) +
    geom_line() +
    geom_point(size = 4) +
    labs(title = 'Investment growth (raw data)',
         x = 'Years',
         y = 'Investment value') +
    scale_colour_brewer(name = 'Investment senario',
                        type = 'qual',
                        palette = 'Dark2') +
    theme_bw(base_size = 16)

# Plot change from baseline investment value
df$change <- df$value - df$starting_value
ggplot(data = df) +
    aes(x = period,
        y = change,
        colour = investment) +
    geom_line() +
    geom_point(size = 4) +
    labs(title = 'Investment growth (change from baseline investment)',
         x = 'Years',
         y = 'Change investment value') +
    scale_colour_brewer(name = 'Investment senario',
                        type = 'qual',
                        palette = 'Dark2') +
    theme_bw(base_size = 16)

# Plot percentage change from baseline investment value
df$percent_change <- 100 * (df$change / df$starting_value)
ggplot(data = df) +
    aes(x = period,
        y = percent_change,
        colour = investment) +
    geom_line() +
    geom_point(size = 4) +
    labs(title = 'Investment growth (percent change from baseline investment)',
         x = 'Years',
         y = 'Percent change investment value (%)',
         caption = "The 'large (2.5% growth)' data are obscured by the 'small (2.5% growth)' data") +
    scale_colour_brewer(name = 'Investment senario',
                        type = 'qual',
                        palette = 'Dark2') +
    theme_bw(base_size = 16)