Q:

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 that laying under my bed and the hypothetical inflation rate is constant at 2% for the next 30 years. Now here 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, or in other words how much of value that $100 lost after all these years? [NOTE: I want the exact value or the percentage of value that I lost from $100 or I want the value that remains after 30 years of inflation (at 2% rate of course).]

A:

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.   

A:

It's just 1-(100/181.14) = 44.79% Lost. 
What remains is 100*(100/181.14) = $55.21

