The Money Mustache Community
Learning, Sharing, and Teaching => Ask a Mustachian => Topic started by: koralcem on September 22, 2014, 02:45:24 PM
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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?
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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.
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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?
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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