Simple & Compound Interest | Interactive Finance Math

Interactive interest model

Principal ($) Annual rate (%) Time (years) Compound frequency

Simple interestCompound interest

Simple interest final balance—

Compound interest final balance—

Simple interest earned—

Compound interest earned—

Extra from compounding—

Compound / simple balance—

What to investigate: With simple interest, the same amount of interest is added each year, so the graph is a straight line. With compound interest, interest is earned on both the original principal and previously earned interest, so the graph curves upward. Try increasing the time or interest rate and watch the gap widen.

Explore Simple and Compound Interest

Change the principal, annual interest rate, investment period and compounding frequency. Observe how the two balances diverge as time increases.

Use the graph to connect the financial formulas with linear and exponential growth.

import numpy as np
import matplotlib.pyplot as plt

# Initial values
P = 10000       # principal
rate = 5        # annual interest rate (%)
t = 20          # years
n = 12          # compounds per year

# Convert percentage to decimal
r = rate / 100

# Simple interest
simple_amount = P * (1 + r*t)
simple_interest = simple_amount - P

# Compound interest
compound_amount = P * (1 + r/n)**(n*t)
compound_interest = compound_amount - P

print("Principal:", P)
print("Simple final balance:", simple_amount)
print("Compound final balance:", compound_amount)
print("Simple interest earned:", simple_interest)
print("Compound interest earned:", compound_interest)
print("Extra from compounding:",
      compound_amount - simple_amount)

# Plot growth over time
years = np.linspace(0, t, 500)

simple = P * (1 + r*years)
compound = P * (1 + r/n)**(n*years)

plt.plot(years, simple,
         label="Simple interest")
plt.plot(years, compound,
         label="Compound interest")

plt.xlabel("Time (years)")
plt.ylabel("Balance")
plt.title("Simple vs Compound Interest")
plt.grid()
plt.legend()
plt.show()

Interest Growth Python Model

This Python model calculates both forms of interest and plots their balances against time. Change the variables and compare the numerical results with the interactive explorer.