Mortgage Prepayment vs. Mutual Fund Investment: A Mathematical Comparison

How Does Debt Payoff Opportunity Costs Work?

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• •Guaranteed Return: Crushing a 6% mortgage yield by paying it down early is basically a guaranteed, tax-free return of exactly 6% on your cash. Pure and simple.
• •Opportunity Yields: Putting that exact same cash into diversified index funds? Historically, that yields about 10% to 12% annually if you stay in it for the long haul.
• •Tax Write-off Deflators: Don't forget that home loan interest payments often count as tax write-offs, which actually reduces the real net rate of your debt.

How Does Mathematical Modeling of Opportunity Cost Spreads Work?

If we really want to model the net yield advantage of throwing cash at the market versus paying down debt, we have to look at the Net Arbitrage Spread after we factor in those marginal tax write-offs:

Let's do some quick math. Imagine your mortgage rate is 6%, your marginal tax rate sits at 30%, and the market return you're expecting is 10%:

So, by tossing that extra cash into the market instead of at the mortgage, you effectively capture a 5.8% net annual compounding advantage on your money.

How Does Technical Python Prepayment vs Market Investment Modeler Work?

Here is a Python quantitative simulator that compares the 20-year net worth outcomes of paying down a home loan against investing in market index funds:

def simulate_mortgage_vs_investment(extra_cash, mortgage_rate, market_rate, tenure_years):
    balance_prepayment = 0.0
    balance_investment = 0.0
    
    # Monthly rates
    r_mortgage = mortgage_rate / 12 / 100
    r_market = market_rate / 12 / 100
    months = tenure_years * 12
    
    for month in range(1, months + 1):
        # prepayment compounds by saving interest
        balance_prepayment = (balance_prepayment + extra_cash) * (1 + r_mortgage)
        # Market compounding
        balance_investment = (balance_investment + extra_cash) * (1 + r_market)
        
    print(f"Prepayment Value: ${balance_prepayment:,.2f} | Market Value: ${balance_investment:,.2f}")
    return balance_prepayment, balance_investment

How Does -Year Net Worth Projection ($500 Monthly Allocation) Work?

The table below breaks down the net worth projections when we pit a 6.0% debt pay-down against a 10.0% market investment: