A tax rate is the proportion applied to taxable income, gains, or withdrawals to determine tax owed. In financial planning, it connects account choice, withdrawal timing, and after-tax wealth. A rate may apply marginally within brackets rather than uniformly across all income. section 9.1.1 section 9.1.2
Use tax rates to evaluate practical decisions:
- Compare pretax IRA and Roth IRA outcomes by distinguishing the current rate, τ₀, from the future withdrawal rate, τₜ. section 9.1.1
- Model bracket effects rather than multiplying total income by one rate; distributing income evenly can avoid pushing earnings into a higher bracket. section 9.1.2
- Account for tax deferral and rate conversion when evaluating tax-loss harvesting, while checking whether future rates could be higher. section 14.1 section 14.1.3
Stable versus uneven income
Assume two brackets: 12% on income from $0 to $100,000 and 22% from $100,000 to $300,000. Income of $50,000 followed by $150,000 produces $29,000 in total tax, while $100,000 in each year produces $24,000. Equal total income can therefore create different tax bills because the marginal rates reached differ. section 9.1.2
Listing 9.2 Computing taxes from income
def calc_taxes(income, TaxTable, deduction):
taxable_income = income - deduction
i = 0
tax = 0
bottom = 0
while taxable_income > bottom:
bracket_income = min(TaxTable.iloc[i]['top_of_bracket'],
taxable_income) - bottom
tax += TaxTable.iloc[i]['rate'] * bracket_income
bottom = TaxTable.iloc[i]['top_of_bracket']
i += 1
return tax
A bracket table and a calc_taxes implementation make marginal-rate calculations explicit: subtract the deduction, process each bracket, and accumulate tax on the income within it. section 9.2.2
