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I am trying to figure out the value of my $100 with a hypothetical 2% constant inflation rate after 30 years.

Here is the scenario: suppose I have $100 laying under my bed and the hypothetical inflation rate is constant at 2% for the next 30 years. I used an online calculator and here is the result:

Forward Flat Rate Inflation Calculator

Now my question is, after all these years and calculation what is the current value of my $100? In other words, how much value of that $100 is lost after all these years? (NOTE: I want the exact value or the percentage of value that I lost from $100 or the value that remains after 30 years of inflation [at the 2% rate].)

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    The site you link also has a backward flat rate calculator
    – Taemyr
    Jun 1, 2020 at 17:31
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    To be a bit pedantic, your $100 will still be worth $100 in 30 years, but it will have the same buying power as $55 (100/181) does today.
    – D Stanley
    Sep 22, 2020 at 13:13

3 Answers 3

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Your $100 at t=0 will be worth $55.2 thirty years hence.

Something that costs $100 today will cost 100*(1.02)^30 = $181 30 years later. So your original $100 can purchase only 100/181 worth of goods that it could purchase at t=0. So its value after 30 years is $100 * 100/181 = $55 in t=0 dollars. So it will have lost 45% of its value in 30 years.

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    @noobforever What does "compound" and "simple" mean to you?
    – user2371765
    May 31, 2020 at 12:32
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    @noobforever What you have typed up is compound. Simple is $102, $104, $106, and so on. Compound grows faster than simple. Inflation applies in a compound manner. The cost 30 years later using compound will be more than the cost 30 years later using simple. So your $100 will lose more value through compound. If you used simple for inflation of 2%, the item will cost you $160. So your $100 will be worth $100*100/160 = $62.5. That is, it will lose only 37.5% of its value. But inflation is always calculated using compound.
    – user2371765
    May 31, 2020 at 12:47
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    @noobforever The link talks about negative rates. Your inflation is positive. If inflation is 2% then what costs $100 today will cost $102 one year later, and 102(1.02) two years later, and so on. Assume you can buy 1 unit of something with $100 today. That 1 unit will cost you $102 one year later. So how much can your $100 that you put under the bed buy you one year later? It is 100/102 units = .9804 units, right? So your $100 lost 1.96% of its value in 1 year.
    – user2371765
    May 31, 2020 at 13:29
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    @noobforever I would suggest that you first understand the dynamics of inflation before you try to do the math. That is, first understand what inflation rate of 2% means. Once you get that, you will do the math right.
    – user2371765
    May 31, 2020 at 13:33
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    1.02^30 is not equal to 1+0.02*30. That's why.
    – user2371765
    Jun 5, 2020 at 13:55
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It's just 1-(100/181.14) = 44.79% Lost.

What remains is 100*(100/181.14) = $55.21

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Took a look at generalising the answers others gave.

Turns out to find out how much your money has been eroded away to due to inflation is just a matter of using a negative value for time in the standard compound interest formula.

100*(1.02)^-30 = 55.21

Same answer as everyone else.

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