# 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 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. 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? 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. 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. 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. May 31, 2020 at 13:33
• 1.02^30 is not equal to 1+0.02*30. That's why. 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

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.