### Author Topic: Compound interest formula for recurring expenses  (Read 3006 times)

#### koralcem

• Posts: 25
##### Compound interest formula for recurring expenses
« on: September 22, 2014, 02:45:24 PM »
Hello,

I'm really new around here, and I'd like to believe I've searched around for to best of my ability before asking, but forgive me if this is a repeat question.

After reading through some articles I wanted to check some of the claims MMM makes about savings across 10 years myself. I've found the compound interest formula, and greatly appreciate the explanation of it at:

http://forum.mrmoneymustache.com/index.php?topic=5979.msg90112#msg90112

But, as far as I can tell, this explains how a given amount, and only the gains from that original amount, compound over time. Can someone explain, just as s l o w l y, how recurring expenses differ from this?

For example, in "The True Cost of Commuting" MMM claims that \$19/day can add up to "about \$125,000" in 10 years:
http://www.mrmoneymustache.com/2011/10/06/the-true-cost-of-commuting/
I'd like to figure out how that number comes about. Because it seems like it's not just \$19 compounding for 10 years. It's \$19 compounding for 10 years, then another \$19 compounding for 9 years and 364 days, and another \$19 compounding for 9 years and 363 days, and so on, right? What's the formula for that series?

#### DollarsAndDissonance

• Posts: 43
• Location: Pacific Northwest, USA
##### Re: Compound interest formula for recurring expenses
« Reply #1 on: September 22, 2014, 03:29:57 PM »
Because it seems like it's not just \$19 compounding for 10 years. It's \$19 compounding for 10 years, then another \$19 compounding for 9 years and 364 days, and another \$19 compounding for 9 years and 363 days, and so on, right? What's the formula for that series?

That's correct; that assumes \$19 put away every day for 10 years.  I wish I could put away \$19 once and have \$125k in 10 years, but alas...

The easiest way to do these calculations is to use a financial calculator.  You can find them online or use Excel's future value formula.  For an 11% return on \$19 a day, you could do =FV(.11/365,3650,-19), which yields \$126,322.

#### koralcem

• Posts: 25
##### Re: Compound interest formula for recurring expenses
« Reply #2 on: September 22, 2014, 10:57:57 PM »
Cool; thanks for the example of using Excel's FV() function. But I'm still curious: does anyone know the actual formula being implemented there?

#### MustachianWays

• Posts: 15
• Age: 32
##### Re: Compound interest formula for recurring expenses
« Reply #3 on: September 23, 2014, 03:09:04 PM »
I think you're looking for the future value of an annuity paid every day, which would be:

Future Value= payment x [ (((1+r)^n) - 1) / r]

r is the interest rate per period
n is the period

Thus:

FV = 19 x [ (((1+.11/365)^(365x10)) - 1) / (.11/365)]
FV = 19 x [ 3.00366821 / .00030137 ]
FV = 19 x 9966.71726
FV = 126322.17
« Last Edit: September 23, 2014, 03:39:21 PM by MustachianWays »