Inflation and the current value of my dollar

Question

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].)

user2371765 · Accepted Answer

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.

base64 · Answer

It's just 1-(100/181.14) = 44.79% Lost.

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

Rohan · Answer

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.

Inflation and the current value of my dollar

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