Pay Off the Mortgage or Invest?

Mortgage

Original loan amount

Interest rate

Term

Years already paid

Early payoff plan

A — Pay the whole balance at once
One lump sum wipes out the loan. B — Extra amount every month
Chips the balance down faster each month.

Extra payment as

Amount / month

Investment

Return, compounded yearly

Years

Match the years to the mortgage payoff date

Tax on investment gains, paid at the end

Difference after 20 years

—

Mortgage — paying it down early

Year	Paid	Interest	Principal	Balance	Net worth

Year	Invested	Growth	Value	Mortgage	Net worth

End of each year, with the early-payoff plan against the original schedule.

With early payoff Original schedule

End of each year, showing money paid in and the resulting market gain or loss.

Money invested Gain Loss

Investments (after tax on gains) minus whatever is still owed on the house. The home’s own value is left out — it is identical under both plans.

Pay the mortgage down Invest the money instead

Both plans commit the same cash each month. Once a plan’s mortgage is gone, the freed-up payment is invested from then on — that is what makes the comparison fair.
The market returns a constant percentage every year. Real returns are not constant, and a bad decade early on hurts far more than this model shows.
Paying the mortgage down is a guaranteed, risk-free return equal to the loan rate. The investment return is not guaranteed. Equal numbers are not equal risk.
Not modelled: property taxes and insurance, PMI removal, mortgage-interest deduction, employer matching, inflation, fees, refinancing, and prepayment penalties.
Tax on gains is applied once, at the end of the period, to growth only.