Monthly Benefit = 1.2 × (Factor A + Factor B) × (1 + 0.05 × n/12)

def nps_deferral_breakeven(base_monthly_krw, deferral_years=5):
    """
    Calculate break-even point for NPS deferral.

    base_monthly_krw: Monthly NPS benefit at normal collection age (KRW in 10,000 units)
    deferral_years: Number of years to defer (1 to 5)
    """
    enhancement_rate = 0.072  # 7.2% per year
    enhanced_monthly = base_monthly_krw * (1 + enhancement_rate * deferral_years)

    # Total amount foregone during deferral period
    foregone_total = base_monthly_krw * 12 * deferral_years

    # Extra monthly income from deferral
    monthly_gain = enhanced_monthly - base_monthly_krw

    # Break-even: months after deferral starts collecting
    breakeven_months = foregone_total / monthly_gain
    breakeven_years = breakeven_months / 12

    print(f"Standard monthly benefit:  {base_monthly_krw:,} (10k KRW)")
    print(f"Deferred monthly benefit:  {enhanced_monthly:,.1f} (10k KRW)")
    print(f"Foregone during deferral:  {foregone_total:,} (10k KRW)")
    print(f"Monthly gain from deferral: {monthly_gain:,.1f} (10k KRW)")
    print(f"Break-even: {breakeven_years:.1f} years after deferred collection begins")
    print(f"=> Profitable if you live {deferral_years + breakeven_years:.1f} years past normal retirement age")

    return breakeven_years

# Example: Standard benefit of 1,200,000 KRW/month, deferring 5 years
nps_deferral_breakeven(base_monthly_krw=120, deferral_years=5)

import numpy as np

def dc_retirement_simulator(
    current_age,
    retirement_age,
    monthly_contribution_krw,  # in 10k KRW units
    current_balance_krw,       # in 10k KRW units
    annual_return_rate,
    inflation_rate=0.025
):
    """
    Simulate DC Retirement Pension accumulation.

    Returns (nominal_future_value, real_future_value) in 10k KRW units.
    """
    years = retirement_age - current_age
    monthly_rate = annual_return_rate / 12
    n_months = years * 12

    # Future value of existing balance
    fv_existing = current_balance_krw * (1 + annual_return_rate) ** years

    # Future value of monthly contributions (annuity formula)
    if monthly_rate > 0:
        fv_contributions = monthly_contribution_krw * (
            ((1 + monthly_rate) ** n_months - 1) / monthly_rate
        )
    else:
        fv_contributions = monthly_contribution_krw * n_months

    nominal_fv = fv_existing + fv_contributions
    real_fv = nominal_fv / (1 + inflation_rate) ** years

    print(f"=== DC Retirement Pension Simulation ===")
    print(f"Age {current_age} → Retire at {retirement_age} ({years} years)")
    print(f"Monthly contribution: {monthly_contribution_krw:,} (10k KRW)")
    print(f"Current balance: {current_balance_krw:,} (10k KRW)")
    print(f"Assumed annual return: {annual_return_rate*100:.1f}%")
    print(f"Inflation assumption: {inflation_rate*100:.1f}%")
    print(f"")
    print(f"Projected balance at retirement (nominal): {nominal_fv:,.0f} (10k KRW)")
    print(f"Projected balance at retirement (real):    {real_fv:,.0f} (10k KRW)")

    return nominal_fv, real_fv

# Example: 35-year-old, retiring at 60, KRW 300k/month, 20M already saved
dc_retirement_simulator(
    current_age=35,
    retirement_age=60,
    monthly_contribution_krw=30,
    current_balance_krw=2000,
    annual_return_rate=0.06
)

def irp_tax_credit_calculator(
    annual_contribution_krw,  # in 10k KRW
    annual_wage_krw           # in 10k KRW
):
    """
    Calculate annual tax credits from IRP + pension savings contributions.
    """
    max_credit_base = 900  # 9,000,000 KRW = 900 in 10k units
    eligible_contribution = min(annual_contribution_krw, max_credit_base)

    if annual_wage_krw <= 5500:  # 55,000,000 KRW
        rate = 0.165
        bracket = "Low (wages <= 55M KRW)"
    else:
        rate = 0.132
        bracket = "Standard (wages > 55M KRW)"

    tax_credit = eligible_contribution * rate

    print(f"Annual wage: {annual_wage_krw * 10:,} KRW → {bracket}")
    print(f"Total contribution: {annual_contribution_krw * 10:,} KRW")
    print(f"Credit-eligible amount: {eligible_contribution * 10:,} KRW")
    print(f"Tax credit rate: {rate*100:.1f}%")
    print(f"Annual tax credit: {tax_credit * 10:,} KRW")
    print(f"Effective return equivalent: {tax_credit / annual_contribution_krw * 100:.1f}%")

    return tax_credit

# Example: 40M KRW annual wage, contributing 9M KRW
print("[ Lower bracket — 55M KRW or below ]")
irp_tax_credit_calculator(annual_contribution_krw=900, annual_wage_krw=4000)
print()

# Example: 70M KRW annual wage, contributing 9M KRW
print("[ Upper bracket — above 55M KRW ]")
irp_tax_credit_calculator(annual_contribution_krw=900, annual_wage_krw=7000)

Pension Savings Fund → up to 6,000,000 KRW/year
IRP → additional 3,000,000 KRW/year
Total → 9,000,000 KRW/year for maximum credit

def isa_transfer_strategy(
    isa_maturity_amount_krw,      # in 10k KRW
    existing_pension_contribution, # in 10k KRW (already paying)
    annual_wage_krw               # in 10k KRW
):
    """
    Model the tax credit effect of transferring ISA proceeds to pension accounts.
    """
    # ISA transfer extra credit base (10% of transfer, capped at 300 = 3M KRW)
    isa_extra_base = min(isa_maturity_amount_krw * 0.10, 300)

    # Standard pension credit base (capped at 900 = 9M KRW)
    pension_base = min(existing_pension_contribution, 900)

    if annual_wage_krw <= 5500:
        rate = 0.165
    else:
        rate = 0.132

    standard_credit = pension_base * rate
    isa_extra_credit = isa_extra_base * rate
    total_credit = standard_credit + isa_extra_credit

    print(f"=== ISA Transfer Strategy ===")
    print(f"ISA maturity amount: {isa_maturity_amount_krw * 10:,} KRW")
    print(f"ISA extra credit base: {isa_extra_base * 10:,} KRW")
    print(f"Standard pension credit base: {pension_base * 10:,} KRW")
    print(f"Credit rate: {rate*100:.1f}%")
    print(f"")
    print(f"Standard pension tax credit: {standard_credit * 10:,} KRW")
    print(f"ISA transfer extra credit: {isa_extra_credit * 10:,} KRW")
    print(f"Total tax credit: {total_credit * 10:,} KRW")

# Example: ISA matures at 30M KRW, standard pension contributions of 9M KRW, wage 50M KRW
isa_transfer_strategy(
    isa_maturity_amount_krw=3000,
    existing_pension_contribution=900,
    annual_wage_krw=5000
)

def compounding_power_demo(
    monthly_investment=50,    # 10k KRW per month
    annual_return=0.07,
    years=30
):
    """
    Illustrate the power of starting early.
    """
    monthly_rate = annual_return / 12
    n = years * 12

    fv = monthly_investment * ((1 + monthly_rate) ** n - 1) / monthly_rate
    total_invested = monthly_investment * n

    print(f"Monthly investment: {monthly_investment * 10:,} KRW")
    print(f"Investment period: {years} years")
    print(f"Annual return: {annual_return * 100:.0f}%")
    print(f"Total contributed: {total_invested * 10:,} KRW")
    print(f"Final balance: {fv * 10:,.0f} KRW")
    print(f"Investment gain: {(fv - total_invested) * 10:,.0f} KRW")
    print(f"Return multiple: {fv / total_invested:.1f}x")

# Starting at 25 vs 35: 10-year head start
print("--- Starting at age 25 (invest for 35 years) ---")
compounding_power_demo(monthly_investment=50, annual_return=0.07, years=35)
print()
print("--- Starting at age 35 (invest for 25 years) ---")
compounding_power_demo(monthly_investment=50, annual_return=0.07, years=25)

def pension_withdrawal_tax(
    annual_withdrawal_krw,  # in 10k KRW
    subscriber_age
):
    """
    Estimate taxes on private pension account withdrawals in Korea.

    Under KRW 15M/year: separate taxation at reduced rates
    Over KRW 15M/year: added to comprehensive income tax base
    """
    THRESHOLD = 1500  # 15M KRW in 10k units

    # Reduced rate by age bracket
    if subscriber_age < 70:
        sep_rate = 0.055
    elif subscriber_age < 80:
        sep_rate = 0.044
    else:
        sep_rate = 0.033

    if annual_withdrawal_krw <= THRESHOLD:
        tax = annual_withdrawal_krw * sep_rate
        tax_method = f"Separate taxation at {sep_rate*100:.1f}%"
    else:
        # Simplified: apply sep rate to threshold, higher rate to excess
        base_tax = THRESHOLD * sep_rate
        excess_tax = (annual_withdrawal_krw - THRESHOLD) * 0.165  # approx comprehensive rate
        tax = base_tax + excess_tax
        tax_method = "Comprehensive income taxation (simplified estimate)"

    after_tax = annual_withdrawal_krw - tax
    effective_rate = tax / annual_withdrawal_krw * 100

    print(f"Annual withdrawal: {annual_withdrawal_krw * 10:,} KRW")
    print(f"Subscriber age: {subscriber_age}")
    print(f"Tax method: {tax_method}")
    print(f"Tax amount: {tax * 10:,.0f} KRW")
    print(f"After-tax income: {after_tax * 10:,.0f} KRW")
    print(f"Effective tax rate: {effective_rate:.2f}%")

# Under the threshold: age 72, 12M KRW/year withdrawal
print("[ Age 72 — Annual 12M KRW withdrawal ]")
pension_withdrawal_tax(annual_withdrawal_krw=1200, subscriber_age=72)
print()

# Over the threshold: age 65, 20M KRW/year withdrawal
print("[ Age 65 — Annual 20M KRW withdrawal ]")
pension_withdrawal_tax(annual_withdrawal_krw=2000, subscriber_age=65)

def full_retirement_model(
    # Demographics
    current_age=35,
    retirement_age=60,
    life_expectancy=90,

    # Current account balances (10k KRW)
    nps_projected_monthly=80,    # Estimated NPS benefit at retirement (today's value)
    dc_balance=1000,
    dc_monthly=25,
    pension_savings_balance=500,
    pension_monthly=50,

    # Return and inflation assumptions
    dc_return=0.05,
    pension_return=0.06,
    inflation=0.025,

    # Monthly living expenses needed in retirement (today's value, 10k KRW)
    monthly_expenses=250
):
    """
    Full retirement income gap analysis across all three pension tiers.
    """
    acc_years = retirement_age - current_age
    dist_years = life_expectancy - retirement_age

    # DC pension at retirement (nominal)
    mr_dc = dc_return / 12
    n_dc = acc_years * 12
    dc_at_retirement = (
        dc_balance * (1 + dc_return) ** acc_years +
        dc_monthly * ((1 + mr_dc) ** n_dc - 1) / mr_dc
    )

    # Pension savings + IRP at retirement (nominal)
    mr_ps = pension_return / 12
    n_ps = acc_years * 12
    ps_at_retirement = (
        pension_savings_balance * (1 + pension_return) ** acc_years +
        pension_monthly * ((1 + mr_ps) ** n_ps - 1) / mr_ps
    )

    total_invested_assets = dc_at_retirement + ps_at_retirement

    # NPS at retirement (adjusted for inflation to reflect nominal future value)
    nps_future_monthly = nps_projected_monthly * (1 + inflation) ** acc_years
    nps_annual = nps_future_monthly * 12

    # Required expenses at retirement (nominal)
    future_monthly_expenses = monthly_expenses * (1 + inflation) ** acc_years
    future_annual_expenses = future_monthly_expenses * 12

    # 4% safe withdrawal rule for invested assets
    annual_withdrawal_dc = dc_at_retirement * 0.04
    annual_withdrawal_ps = ps_at_retirement * 0.04
    total_annual_income = annual_withdrawal_dc + annual_withdrawal_ps + nps_annual

    income_gap = future_annual_expenses - total_annual_income

    print("=" * 55)
    print("     COMPREHENSIVE RETIREMENT INCOME PROJECTION")
    print("=" * 55)
    print(f"Current age: {current_age} | Retirement: {retirement_age} | Life exp: {life_expectancy}")
    print(f"Accumulation period: {acc_years} years | Distribution: {dist_years} years")
    print()
    print("[Projected Assets at Retirement]")
    print(f"  DC Retirement Pension:   {dc_at_retirement:>12,.0f} (10k KRW)")
    print(f"  Pension Savings + IRP:   {ps_at_retirement:>12,.0f} (10k KRW)")
    print(f"  Total Invested Assets:   {total_invested_assets:>12,.0f} (10k KRW)")
    print()
    print("[Projected Annual Income at Retirement]")
    print(f"  DC account (4% rule):    {annual_withdrawal_dc:>12,.0f} (10k KRW/yr)")
    print(f"  Pension savings (4%):    {annual_withdrawal_ps:>12,.0f} (10k KRW/yr)")
    print(f"  NPS benefit:             {nps_annual:>12,.0f} (10k KRW/yr)")
    print(f"  Total Income:            {total_annual_income:>12,.0f} (10k KRW/yr)")
    print()
    print("[Annual Expenses at Retirement (Nominal)]")
    print(f"  Monthly (nominal):       {future_monthly_expenses:>12,.0f} (10k KRW)")
    print(f"  Annual (nominal):        {future_annual_expenses:>12,.0f} (10k KRW)")
    print()
    if income_gap > 0:
        print(f"[WARNING] Annual income shortfall: {income_gap:,.0f} (10k KRW)")
        print("  => Consider increasing contributions or adjusting spending plans.")
    else:
        print(f"[ON TRACK] Annual income surplus: {-income_gap:,.0f} (10k KRW)")
        print("  => Current plan appears sufficient for your retirement goal.")

# Run a baseline scenario for a 35-year-old
full_retirement_model()