I’ve been slowly making my way through Mr. Money Mustache’s blog archive — something I encourage everyone to check out — and it’s been an incredibly eye opening experience.
Take this, for example:
A Starbucks habit of picking up a regular coffee and biscotti on the way to work each workday. $4/day = $20/week = $15,040 in coffee over just ten years!!
Without compounding, $4/day = $20/week = $1,040/year or $10,400 after ten years. However, to calculate it’s actual future value you have to take into account what would happen if you invested that $20/week instead.
He provides a helpful shortcut for calculating the future value assuming 7% growth compounded over 10 years:
To calculate a weekly expense compounded over ten years, multiply the price by 752. For a monthly expense, multiply by 173.
752 * $20 equals the $15,040 he calculated.
Curious, I looked into the math behind this. He provides a link to Future Value Calculator which derives the formula for an ordinary annuity, though I found this explanation on Investopedia much easier to follow.
Where does that 752 come from? From the Investopedia article:
In this case the interest is not 7% but 7% divided by 52 weeks per year, and the number of payments is 52 weeks per year multiplied by 10 years.
The future value then is:
Or, more simply:
That’s where the 752 comes from.
Similarly, the future value after 10 years of monthly savings is:
What’s amazing is that $15K is just by saving $20/week. If you can save $100/week instead, you’ll net about $75,200 after ten years. Pretty crazy isn’t it?