Rule of 72 Accuracy Plot

rule_of_72_accuracy_plot.py

"""
Plotting the accuracty of the rule of 72.

https://en.wikipedia.org/wiki/Rule_of_72
"""

import math

import matplotlib.pyplot as plt


def rule_of_72(rate: float):
    return 72 / rate


def actual_doubling_time(rate):
    return math.log(2) / math.log(1 + rate / 100)


rates = [r / 10 for r in range(30, 201)]


rule_of_72_values = [rule_of_72(rate) for rate in rates]
actual_doubling_time_values = [actual_doubling_time(rate) for rate in rates]

# Now plot the accuracy with a separate y-axis on the right
fig, ax1 = plt.subplots()
plt.title("The Rule of 72 Accuracy")

ax1.set_ylabel("Doubling time")
ax1.plot(rates, actual_doubling_time_values, label="Actual doubling time", color="orange")
ax1.plot(rates, rule_of_72_values, label="Rule of 72", color="blue")
ax1.set_xlabel("Rate of return (%)")
ax1.legend(loc="upper left")


ax2 = ax1.twinx()
ax2.set_ylabel("Ratio")
ax2.plot(
    rates,
    [(a / r) for a, r in zip(actual_doubling_time_values, rule_of_72_values, strict=False)],
    label="Ratio",
    color="red",
)
ax2.legend(loc="upper right")


plt.show()