The formula
Future value = monthly contribution × ((1 + i)ⁿ − 1) / i
Where it comes from
A small, frequent expense is invisible by definition: four pounds go unnoticed, and a thousand a year does not. The first figure here is that total, and it usually surprises. The second is what that same money, set aside monthly and invested, would grow into over the years, which is the future value of a constant stream of contributions.
How to work it out by hand
- Multiply the daily spend by the days a week you repeat it and by 52
- Divide by twelve for the monthly equivalent
- Apply the future value formula for a regular contribution
- Compare that result with what you will have contributed in total
What is worth knowing
The rhetorical trick in these sums is the term and the return: over thirty years at seven per cent, any small expense turns into a scandalous figure. It is true and also inflated, because the figure is in future money and because it assumes that saving really would have been invested every month for thirty years, which almost nobody does. Use it for the order of magnitude, not as a reproach.