Notebook exploring compound interest

compound-interest.Rmd

---
title: "Compound interest calculator"
---

Terms are defined as:

 * Principal - Initial amount invested
 * Contribution - How much is contributed in each period
 * Interest - Interest rate
 * Period - How frequently interest is compounded

```{r}
suppressPackageStartupMessages(library(tidyverse))
suppressPackageStartupMessages(library(lubridate))

input <- list(
  principal    =   0.00,
  contribution = 250.00,
  interest     =   0.02,
  period       = "month",
  from         = as_date("2019-01-01"),
  until        = as_date("2019-01-01") + years(10)
)
```

# Do the calculation

See www.thecalculatorsite.com/articles/finance/compound-interest-formula.php?page=2

```{r}

compound_principal <- function(principal, rate, p, time) {
  t <- time_length(time, "years")
  n <- years(1) / period(p)
  
  principal * (1 + rate/n)^(n*t)
}

future_value <- function(contribution, rate, p, time) {
  t <- time_length(time, "years")
  n <- years(1) / period(p)
  
  contribution * (((1 + rate/n)^(n * t) - 1) / (rate/n)) * (1 + rate/n)
}

calc_balance <- function(principal, contribution, rate, p, time) {
  principal_value <- compound_principal(principal, rate, p, time)
  contrbution_value <- future_value(contribution, rate, p, time)
  
  principal_value + contrbution_value
}


project_balance <- function(input) {
  compounded_balance <- 
    tibble(!!!input,
           date = seq(input$from, input$until, by = "1 month")) %>% 
    mutate(amount = calc_balance(
      input$principal, 
      input$contribution,
      input$interest,
      input$period,
      date - input$from
    ))
  
  compounded_balance
}
```

What about for various different scenarios...

```{r}
parameter <- "interest"
values <- c(0.0125, 0.02, 0.05)

values %>% 
  map(~ magrittr::inset(input, parameter, .x)) %>% 
  map_dfr(project_balance) %>% 
  mutate(parameter := pull(., !!parameter)) %>% 
  ggplot(aes(x = date, y = amount)) +
  geom_path() +
  geom_hline(yintercept = 0, colour = "dimgray") +
  scale_y_continuous(labels = scales::dollar_format(prefix = "£")) +
  expand_limits(y = 0)  +
  theme_minimal() +
  labs(title = "Savings balance",
       subtitle = str_glue("Starting with £{input$principal}, ",
                           "contributing £{input$contribution} per ",
                           "{input$period}"),
       x = NULL,
       y = NULL) +
  facet_wrap(~ parameter)
```