Rule of 72 Calculator

import math

def rule_of_72(rate: float) -> float:
    """Estimate years to double using Rule of 72."""
    if rate <= 0:
        raise ValueError("Rate must be positive")
    return 72 / rate

def exact_doubling_time(rate: float) -> float:
    """Exact years to double using logarithm formula."""
    if rate <= 0:
        raise ValueError("Rate must be positive")
    return math.log(2) / math.log(1 + rate / 100)

# Example
rate = 6  # 6% annual return
years_72 = rule_of_72(rate)
years_exact = exact_doubling_time(rate)

print(f"Rule of 72: {years_72:.1f} years")     # 12.0 years
print(f"Exact formula: {years_exact:.2f} years") # 11.90 years

# Table for common rates
print("\nRate | Rule of 72 | Exact")
for r in [2, 4, 6, 8, 10, 12]:
    print(f" {r:2d}% |  {rule_of_72(r):5.1f} yrs | {exact_doubling_time(r):.2f} yrs")