The Fed wants money to be about half as valuable, every 30 years give or take one or two, on account of inflation. Learn how to estimate the pace of inflation with a simple exponential equation that can reveal information both about the past and the future.
Between 1995 and 2019—before the economic effects of the COVID-19 pandemic—the average annual inflation rate in the US was 2.18%. This is close to what the Fed wants to happen every year, and when there isn’t a major disease ravaging the world, it’s a pretty good average of the inflation rate of the modern US economy. Prices go up some—low inflation like that is natural and helps the economy grow, year over year—but the process isn’t a runaway train without anyone at the controls.
One can find how much less their money is worth by simply plugging in a few numbers into a simple exponential function: take the quantity (1 + the inflation rate) and raise it to the power of the number of years you want to move. Use a positive number in the exponent to look in the future, and a negative number in the exponent to look in the past. Multiply this by the amount of money you want to have in your base year.
Let’s try two examples:
The average rate of inflation going back to 1950, we have been told, is 3.53%, and we want to see the change from 1950 going forward to 2023 on $1000. That is, how much money in 2023 terms would we need to have the equivalent of $1000 in 1950 terms? That would simply be the result of (1000)(1.0353)^ (2023-1950). We start with $1000 in 1950, and we multiply that number by the 3.53% inflation factor (keeping all our previous money with each multiplication) as many times as there are years between 2023 and 1950. Doing this calculation, and rounding the result a bit, we see that $1,000 in 1950 has inflated to about $12,600 in 2023. You need about $12,600 in 2023 to buy now what $1,000 could have bought you in 1950.
Going the other way, let’s see what $1000 today would have bought you in 1950. The equation looks the same, except we want to go back in time, so we reverse the order of the subtraction in the exponent: 1000(1.0353)^(1950-2023), and we get that $1000 in 2023 would have been the equivalent of about $80 in 1950, after some rounding.
Now that we are comfortable going both ways, let’s see how long it takes for the two ways to give us 2 and ½, respectively, if we assume an inflation rate of 2.2% (about what it’s been in the real world since 1995)
There are more rigorous ways to solve this, but for the purposes of experimentation and gaining familiarity with the setup, simply plug in a year and adjust if that value is too far from $500 to go back in time: 1000*(1.022)^(something smaller – 2022)
Plugging in 1991, we see that our current $1000 would hypothetically be worth the same as $498.39 would have been worth in 1991, so assuming a 2.2% inflation rate, some amount of money in today’s dollars would buy twice as much in 1991 as it would today. (The actual value of those $1000 in 2023, but in 1991 terms is slightly less than that, so the actual rate of inflation from 1991 to 2023 was slightly higher than we assumed, but this is only a practice exercise with hypothetical numbers. The actual year in which the result would be closest to $500 was 1995 basesd on real data)
Going forward in time, the setup is the same. We will assume for simplicity’s sake the same rate of inflation continues to hold, on average, indefinitely into the future. If that’s true, then what we could buy for $1000 in 2023, will cost us $2,006.45 in 2055.
So, we can see that, should we travel back in time from 1991, our money will buy us roughly twice as much when we get out of the time machine as it would back home, and if we take the time machine forward to 2055, our money will probably only buy us roughly half as much as it would back home.
Between 1995 and 2019—before the economic effects of the COVID-19 pandemic—the average annual inflation rate in the US was 2.18%. This is close to what the Fed wants to happen every year, and when there isn’t a major disease ravaging the world, it’s a pretty good average of the inflation rate of the modern US economy. Prices go up some—low inflation like that is natural and helps the economy grow, year over year—but the process isn’t a runaway train without anyone at the controls.
One can find how much less their money is worth by simply plugging in a few numbers into a simple exponential function: take the quantity (1 + the inflation rate) and raise it to the power of the number of years you want to move. Use a positive number in the exponent to look in the future, and a negative number in the exponent to look in the past. Multiply this by the amount of money you want to have in your base year.
Let’s try two examples:
The average rate of inflation going back to 1950, we have been told, is 3.53%, and we want to see the change from 1950 going forward to 2023 on $1000. That is, how much money in 2023 terms would we need to have the equivalent of $1000 in 1950 terms? That would simply be the result of (1000)(1.0353)^ (2023-1950). We start with $1000 in 1950, and we multiply that number by the 3.53% inflation factor (keeping all our previous money with each multiplication) as many times as there are years between 2023 and 1950. Doing this calculation, and rounding the result a bit, we see that $1,000 in 1950 has inflated to about $12,600 in 2023. You need about $12,600 in 2023 to buy now what $1,000 could have bought you in 1950.
Going the other way, let’s see what $1000 today would have bought you in 1950. The equation looks the same, except we want to go back in time, so we reverse the order of the subtraction in the exponent: 1000(1.0353)^(1950-2023), and we get that $1000 in 2023 would have been the equivalent of about $80 in 1950, after some rounding.
Now that we are comfortable going both ways, let’s see how long it takes for the two ways to give us 2 and ½, respectively, if we assume an inflation rate of 2.2% (about what it’s been in the real world since 1995)
There are more rigorous ways to solve this, but for the purposes of experimentation and gaining familiarity with the setup, simply plug in a year and adjust if that value is too far from $500 to go back in time: 1000*(1.022)^(something smaller – 2022)
Plugging in 1991, we see that our current $1000 would hypothetically be worth the same as $498.39 would have been worth in 1991, so assuming a 2.2% inflation rate, some amount of money in today’s dollars would buy twice as much in 1991 as it would today. (The actual value of those $1000 in 2023, but in 1991 terms is slightly less than that, so the actual rate of inflation from 1991 to 2023 was slightly higher than we assumed, but this is only a practice exercise with hypothetical numbers. The actual year in which the result would be closest to $500 was 1995 basesd on real data)
Going forward in time, the setup is the same. We will assume for simplicity’s sake the same rate of inflation continues to hold, on average, indefinitely into the future. If that’s true, then what we could buy for $1000 in 2023, will cost us $2,006.45 in 2055.
So, we can see that, should we travel back in time from 1991, our money will buy us roughly twice as much when we get out of the time machine as it would back home, and if we take the time machine forward to 2055, our money will probably only buy us roughly half as much as it would back home.
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