How the math works

Every number on this site is an illustration, not a forecast. The formulas are the same ones a spreadsheet uses. The assumptions are yours to change.

Recurring savings

A daily coffee is converted to an annual amount (amount × times × periods in a year). That annual figure is treated as twelve equal monthly deposits. Those deposits earn a constant annual return, compounded monthly — the future value of an ordinary annuity:

FV = PMT × ((1 + r)ⁿ − 1) / r

PMT is the monthly deposit, r is the monthly rate (annual ÷ 12), and n is the number of months in your horizon. The dashed line on the chart is the same deposits with r = 0: cash in a drawer.

Mortgage overpayments

The scheduled payment uses the standard amortization formula. We then walk the loan month by month. Extra principal is applied after that month’s interest, so the balance falls faster, the term shortens, and total interest shrinks. The “invest instead” figure asks: what if that extra cash bought index funds at your assumed return for the shortened term?

Travel class and one-time choices

A fare difference that repeats (two long-haul trips a year) is an annuity. A one-time gap (used car vs new, a simpler wedding) is a lump sum grown at (1 + r)ⁿ. Neither model prices comfort, status, or joy. It only prices the money.

What we leave out

• Inflation (figures are nominal, not inflation-adjusted).
• Taxes on interest, dividends, and capital gains.
• Fees, sequence-of-returns risk, and the fact that 7% is not a promise.
• Mortgage tax deduction, PMI removal, or refinance options.
• The value of an experience you actually wanted.

Default return is 7% because it is a round, widely cited long-run equity illustration. Move the slider. If you use 4%, the story is quieter and still worth reading.