How to calculate compound interest in R

statistics

compound interest

Learn calculate compound interest in r with clear examples and explanations.

Published

March 26, 2026

Introduction

Compound interest is one of the most powerful concepts in finance - it’s the process where your investment earns returns not just on the initial amount, but also on all previously earned interest. In this tutorial, we’ll use R and the tidyverse to calculate, analyze, and visualize compound interest scenarios to help you understand how investments grow over time.

Setting Up Our Analysis

First, let’s load the required packages and set up our basic parameters for compound interest calculations.

library(tidyverse)
library(scales)
library(gt)
theme_set(theme_bw(16))

Now we’ll define our initial investment scenario with clear, realistic parameters.

principal <- 1000    # Starting amount
years <- 10          # Time period in years
rate <- 0.05         # Interest rate (5%)

These variables represent a $1,000 investment over 10 years at 5% annual interest - a common scenario for understanding compound growth.

Creating the Basic Data Structure

Let’s start by creating a tibble with years from 0 to 10 to track our investment over time.

tibble(year = 0:years)

This creates our foundation - a simple table with one column showing each year of our investment period.

Calculating Compound Interest

Now we’ll add the compound interest calculation using the standard formula: A = P(1 + r)^t.

compound_data <- tibble(year = 0:years) |>
  mutate(amount = principal * (1 + rate) ^ year)

The amount column now shows how our $1,000 grows each year, with interest compounding annually.

Adding Interest Earned

Let’s enhance our analysis by calculating how much interest we’ve earned above our initial investment.

compound_data <- tibble(year = 0:years) |>
  mutate(
    amount = principal * (1 + rate) ^ year,
    interest_earned = amount - principal
  )

print(compound_data)

The interest_earned column shows the cumulative interest gained, making it easy to see the power of compounding over time.

Visualizing Single Investment Growth

A line chart helps visualize how compound interest accelerates over time.

compound_data |>
  ggplot(aes(x = year, y = amount)) +
  geom_line(color = "blue", linewidth = 1) +
  geom_point(color = "red", size = 2) +
  labs(
    title = paste("Compound Interest Over", years, "Years"),
    x = "Year",
    y = "Investment Value",
    subtitle = paste("Starting with $", scales::comma(principal), "at", rate * 100, "% annual interest")
  ) +
  scale_y_continuous(labels = label_currency())

Line chart of a $1,000 investment growing at 5 percent annual compound interest over ten years in R, with yearly dots on the curve showing the accelerating exponential growth of principal plus interest produced by the formula A = P(1 + r)^t.

This visualization clearly shows the exponential nature of compound growth - notice how the curve gets steeper in later years.

Scaling Up: Larger Investment Example

Let’s see how compound interest works with a larger investment amount like $500,000.

principal_large <- 500000
years <- 10
rate <- 0.05

large_investment <- tibble(year = 0:years) |>
  mutate(
    amount = principal_large * (1 + rate) ^ year,
    interest_earned = amount - principal_large
  )

With a larger principal, the absolute dollar growth becomes much more dramatic, though the percentage growth remains the same.

Visualizing the Larger Investment

large_investment |>
  ggplot(aes(x = year, y = amount)) +
  geom_line(color = "green4", linewidth = 1) +
  geom_point(color = "red", size = 2) +
  labs(
    title = "Compound Interest: $500K Investment",
    x = "Year",
    y = "Investment Value",
    subtitle = paste("Growth at", rate * 100, "% annual interest")
  ) +
  scale_y_continuous(labels = label_currency())

Line chart of a $500,000 investment growing at 5 percent annual compound interest over ten years in R, with currency-formatted y-axis showing how a large principal compounds into substantially larger absolute dollar growth every year.

The same 5% rate now generates tens of thousands in additional value each year due to the larger base amount.

Comparing Multiple Interest Rates

Real investments have varying returns, so let’s compare different interest rate scenarios.

rates <- seq(0.04, 0.10, by = 0.02)  # 4%, 6%, 8%, 10%
principal <- 500000
years <- 10

These rates represent a realistic range from conservative (4%) to optimistic (10%) annual returns.

Creating Multi-Rate Comparison Data

We’ll use expand_grid() to create all combinations of years and interest rates.

multi_rate_data <- expand_grid(year = 0:years, rate = rates) |>
  mutate(
    amount = principal * (1 + rate) ^ year,
    interest_earned = amount - principal
  )

This creates a comprehensive dataset showing how the same investment performs under different interest rate scenarios.

Visualizing Rate Comparisons

multi_rate_data |>
  ggplot(aes(x = year, y = amount, color = factor(rate))) +
  geom_line(linewidth = 1) +
  geom_point(size = 2) +
  labs(
    title = "Compound Interest: Impact of Different Rates",
    x = "Year",
    y = "Investment Value",
    color = "Interest Rate",
    subtitle = paste("Starting investment: $", scales::comma(principal))
  ) +
  scale_y_continuous(labels = label_currency())

Multi-line chart comparing $500,000 compound interest growth over ten years at 4, 6, 8, and 10 percent annual rates in R, dramatically showing how small rate differences produce large gaps in final portfolio value by year ten.

This comparison dramatically shows how even small differences in interest rates (like 2%) can result in huge differences in final value over time.

Creating a Comparison Table

For precise comparisons, let’s create a formatted table showing values at each rate.

multi_rate_data |>
  select(year, rate, amount) |>
  pivot_wider(
    names_from = rate, 
    values_from = amount,
    names_glue = "{rate*100}% Rate"
  ) |>
  gt() |>
  fmt_currency(columns = -year)

This table format makes it easy to compare exact dollar amounts across different scenarios and time periods.

Summary

Compound interest calculations in R demonstrate the powerful concept of exponential growth over time. Using tidyverse tools like tibble(), mutate(), and expand_grid(), we can easily model different investment scenarios and visualize how small changes in interest rates or time periods create dramatic differences in outcomes. The key insight is that compound interest rewards both higher rates and longer time horizons, with the effects becoming more pronounced as investments mature. These R techniques can be applied to any financial planning scenario, from retirement savings to loan calculations.

--- title: "How to calculate compound interest in R" description: "Learn calculate compound interest in r with clear examples and explanations." date: 2026-03-26 categories: ['statistics', 'compound interest'] format: html: code-fold: false code-tools: true --- ## Introduction Compound interest is one of the most powerful concepts in finance - it's the process where your investment earns returns not just on the initial amount, but also on all previously earned interest. In this tutorial, we'll use R and the tidyverse to calculate, analyze, and visualize compound interest scenarios to help you understand how investments grow over time. ## Setting Up Our Analysis First, let's load the required packages and set up our basic parameters for compound interest calculations. ```r library(tidyverse) library(scales) library(gt) theme_set(theme_bw(16)) ``` Now we'll define our initial investment scenario with clear, realistic parameters. ```r principal <- 1000 # Starting amount years <- 10 # Time period in years rate <- 0.05 # Interest rate (5%) ``` These variables represent a $1,000 investment over 10 years at 5% annual interest - a common scenario for understanding compound growth. ## Creating the Basic Data Structure Let's start by creating a tibble with years from 0 to 10 to track our investment over time. ```r tibble(year = 0:years) ``` This creates our foundation - a simple table with one column showing each year of our investment period. ## Calculating Compound Interest Now we'll add the compound interest calculation using the standard formula: A = P(1 + r)^t. ```r compound_data <- tibble(year = 0:years) |> mutate(amount = principal * (1 + rate) ^ year) ``` The `amount` column now shows how our $1,000 grows each year, with interest compounding annually. ## Adding Interest Earned Let's enhance our analysis by calculating how much interest we've earned above our initial investment. ```r compound_data <- tibble(year = 0:years) |> mutate( amount = principal * (1 + rate) ^ year, interest_earned = amount - principal ) print(compound_data) ``` The `interest_earned` column shows the cumulative interest gained, making it easy to see the power of compounding over time. ## Visualizing Single Investment Growth A line chart helps visualize how compound interest accelerates over time. ```r compound_data |> ggplot(aes(x = year, y = amount)) + geom_line(color = "blue", linewidth = 1) + geom_point(color = "red", size = 2) + labs( title = paste("Compound Interest Over", years, "Years"), x = "Year", y = "Investment Value", subtitle = paste("Starting with $", scales::comma(principal), "at", rate * 100, "% annual interest") ) + scale_y_continuous(labels = label_currency()) ``` ![Line chart of a $1,000 investment growing at 5 percent annual compound interest over ten years in R, with yearly dots on the curve showing the accelerating exponential growth of principal plus interest produced by the formula A = P(1 + r)^t.](/images/statistics/compound-interest-in-r-1k-growth-curve-ggplot.png) This visualization clearly shows the exponential nature of compound growth - notice how the curve gets steeper in later years. ## Scaling Up: Larger Investment Example Let's see how compound interest works with a larger investment amount like $500,000. ```r principal_large <- 500000 years <- 10 rate <- 0.05 large_investment <- tibble(year = 0:years) |> mutate( amount = principal_large * (1 + rate) ^ year, interest_earned = amount - principal_large ) ``` With a larger principal, the absolute dollar growth becomes much more dramatic, though the percentage growth remains the same. ## Visualizing the Larger Investment ```r large_investment |> ggplot(aes(x = year, y = amount)) + geom_line(color = "green4", linewidth = 1) + geom_point(color = "red", size = 2) + labs( title = "Compound Interest: $500K Investment", x = "Year", y = "Investment Value", subtitle = paste("Growth at", rate * 100, "% annual interest") ) + scale_y_continuous(labels = label_currency()) ``` ![Line chart of a $500,000 investment growing at 5 percent annual compound interest over ten years in R, with currency-formatted y-axis showing how a large principal compounds into substantially larger absolute dollar growth every year.](/images/statistics/compound-interest-in-r-500k-growth-curve-ggplot.png) The same 5% rate now generates tens of thousands in additional value each year due to the larger base amount. ## Comparing Multiple Interest Rates Real investments have varying returns, so let's compare different interest rate scenarios. ```r rates <- seq(0.04, 0.10, by = 0.02) # 4%, 6%, 8%, 10% principal <- 500000 years <- 10 ``` These rates represent a realistic range from conservative (4%) to optimistic (10%) annual returns. ## Creating Multi-Rate Comparison Data We'll use `expand_grid()` to create all combinations of years and interest rates. ```r multi_rate_data <- expand_grid(year = 0:years, rate = rates) |> mutate( amount = principal * (1 + rate) ^ year, interest_earned = amount - principal ) ``` This creates a comprehensive dataset showing how the same investment performs under different interest rate scenarios. ## Visualizing Rate Comparisons ```r multi_rate_data |> ggplot(aes(x = year, y = amount, color = factor(rate))) + geom_line(linewidth = 1) + geom_point(size = 2) + labs( title = "Compound Interest: Impact of Different Rates", x = "Year", y = "Investment Value", color = "Interest Rate", subtitle = paste("Starting investment: $", scales::comma(principal)) ) + scale_y_continuous(labels = label_currency()) ``` ![Multi-line chart comparing $500,000 compound interest growth over ten years at 4, 6, 8, and 10 percent annual rates in R, dramatically showing how small rate differences produce large gaps in final portfolio value by year ten.](/images/statistics/compound-interest-in-r-multi-rate-comparison-ggplot.png) This comparison dramatically shows how even small differences in interest rates (like 2%) can result in huge differences in final value over time. ## Creating a Comparison Table For precise comparisons, let's create a formatted table showing values at each rate. ```r multi_rate_data |> select(year, rate, amount) |> pivot_wider( names_from = rate, values_from = amount, names_glue = "{rate*100}% Rate" ) |> gt() |> fmt_currency(columns = -year) ``` This table format makes it easy to compare exact dollar amounts across different scenarios and time periods. ## Summary Compound interest calculations in R demonstrate the powerful concept of exponential growth over time. Using tidyverse tools like `tibble()`, `mutate()`, and `expand_grid()`, we can easily model different investment scenarios and visualize how small changes in interest rates or time periods create dramatic differences in outcomes. The key insight is that compound interest rewards both higher rates and longer time horizons, with the effects becoming more pronounced as investments mature. These R techniques can be applied to any financial planning scenario, from retirement savings to loan calculations.