# Saving $X Per Week Nets You$752X After 10 Years

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:

$FV = C*[ \frac{(1+\frac{0.07}{52})^{52*10}-1}{\frac{0.07}{52}} ]$

Or, more simply:

$FV = C * 752.34$

That’s where the 752 comes from.

Similarly, the future value after 10 years of monthly savings is:

$FV = C*[ \frac{(1+\frac{0.07}{12})^{12*10}-1}{\frac{0.07}{12}} ]$

$FV = C * 173.08$

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?
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