How to Compute Compound Interest with Tidyverse

Compound Interest
Learn how to compute compound interest with Tidyverse in R. Practical tutorial with examples.
Published

September 27, 2024

Compound interest calculations are essential for financial planning and investment analysis. The tidyverse provides powerful tools for computing compound interest across different time periods and scenarios, making it easy to visualize and compare investment growth.

Getting Started

library(tidyverse)
library(palmerpenguins)

Example 1: Basic Compound Interest Calculation

The Problem

You want to calculate how a $1000 investment grows over 10 years with 7% annual interest. We need to compute the compound interest formula: A = P(1 + r)^t.

Step 1: Create the Investment Data

We’ll start by setting up our basic investment parameters.

investment <- tibble(
  principal = 1000,
  rate = 0.07,
  years = 10
)

This creates a data frame with our initial investment amount, interest rate, and time period.

Step 2: Calculate Final Amount

Now we’ll apply the compound interest formula using mutate().

investment <- investment |>
  mutate(
    final_amount = principal * (1 + rate)^years,
    total_interest = final_amount - principal
  )

The investment grows to $1967.15 with $967.15 in compound interest earned.

Step 3: View the Results

Let’s examine our calculation results.

investment |>
  select(principal, final_amount, total_interest) |>
  mutate(across(where(is.numeric), ~ round(.x, 2)))

This shows the principal, final amount, and total interest earned in a clean format.

Example 2: Comparing Multiple Investment Scenarios

The Problem

You want to compare different investment strategies with varying principals, interest rates, and time periods. This helps you understand how different factors affect compound growth and make informed investment decisions.

Step 1: Create Multiple Scenarios

We’ll set up different investment scenarios to compare.

scenarios <- tibble(
  scenario = c("Conservative", "Moderate", "Aggressive"),
  principal = c(5000, 10000, 15000),
  annual_rate = c(0.04, 0.07, 0.10),
  years = c(20, 15, 10)
)

Each scenario represents a different risk-return profile with varying investment amounts and rates.

Step 2: Calculate Growth Over Time

Now we’ll expand each scenario to show year-by-year growth.

yearly_growth <- scenarios |>
  rowwise() |>
  mutate(
    year_data = list(1:years),
    .keep = "all"
  ) |>
  unnest(year_data)

This creates a row for each year in each investment scenario for detailed tracking.

Step 3: Compute Annual Values

We’ll calculate the investment value for each year.

yearly_growth <- yearly_growth |>
  mutate(
    amount = principal * (1 + annual_rate)^year_data,
    interest_earned = amount - principal
  )

Now we have the compound growth calculated for each year across all scenarios.

Step 4: Visualize the Growth

Let’s create a visualization to compare the scenarios.

yearly_growth |>
  ggplot(aes(x = year_data, y = amount, color = scenario)) +
  geom_line(size = 1.2) +
  labs(title = "Compound Interest Growth Comparison",
       x = "Years", y = "Investment Value ($)")

Line plot comparing compound interest growth across conservative moderate and aggressive investment scenarios in R

The plot clearly shows how different rates and principals affect long-term growth.

Step 5: Summary Statistics

Finally, we’ll calculate summary statistics for each scenario.

scenario_summary <- yearly_growth |>
  group_by(scenario) |>
  summarise(
    final_value = max(amount),
    total_return = max(interest_earned),
    avg_annual_growth = (max(amount) / principal[1])^(1/max(year_data)) - 1
  )

This provides key metrics to compare the effectiveness of each investment strategy.

Summary

  • Use mutate() with the compound interest formula A = P(1 + r)^t to calculate investment growth
  • Create multiple scenarios with tibble() and compare different investment strategies side by side
  • Expand data with unnest() and rowwise() operations to show year-by-year compound growth
  • Visualize compound interest trends using ggplot2 to identify optimal investment approaches

  • Generate summary statistics with group_by() and summarise() to compare final values and returns across scenarios