# Inflation and the current value of my dollar

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:

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].) • The site you link also has a backward flat rate calculator Commented Jun 1, 2020 at 17:31 • 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. Commented Sep 22, 2020 at 13:13

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. • @noobforever What does "compound" and "simple" mean to you? Commented May 31, 2020 at 12:32 • @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. Commented May 31, 2020 at 12:47 • @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. Commented May 31, 2020 at 13:29 • @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. Commented May 31, 2020 at 13:33 • 1.02^30 is not equal to 1+0.02*30. That's why. Commented Jun 5, 2020 at 13:55 It's just 1-(100/181.14) = 44.79% Lost. What remains is 100*(100/181.14) =$55.21