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Old 03-26-2012, 02:19 AM   #81
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If inflation was 5% then at the end of the first year you'd have 95 cents. Doing it nine more times would leave 63 cents.

Getting it down to 50 cents would require about 14.4 years by the Rule of 72, although the actual number turns out to be about 14.206699 years.
Thanks Nords, good catch.

I typed: ".....the prospect of moderate inflation causing the purchasing power of their non-COLA'd pension to drop by 50% over the next decade."

I was thinking: ".....the prospect of moderate inflation causing prices to increase by 50% over the next decade." That would have been the "moderate" inflation between 4% and 5% I mentioned.

My bad. And my apologies to you and the board participants.
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Old 03-26-2012, 05:08 AM   #82
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If inflation was 5% then at the end of the first year you'd have 95 cents. Doing it nine more times would leave 63 cents.
I calculate that after 10 iterations, you'd have 59.874 cents (0.95 ** 10, or 0.95 ^ 10 as the kids say these days ).

However, if inflation is defined as an increase in prices, then the corollary of 5% inflation is that after a year, $1 is worth not $0.95, but ($1 / 1.05) = 95.258 cents. Compound that nine further times (10 in total) and you end up with (0.95258 ** 10) = 61.391 cents.

You can check that by calculating (1.05 ** 10) = 1.62889 (that is, $1 invested at 5% compound with no deductions would give you $1.62889 after 10 years), and divide that into 1 => 1.0/1.62889 = 0.61391.
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Old 03-26-2012, 05:39 AM   #83
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I hate to say it but I think this is inevitable. I just hope it doesn't come more rapidly than we can adjust to it. And in reality, I don't know that our standard of living is falling as much as it is that others are more quickly catching up to us while we are running in place (or slowly backpedaling).
It's falling, because the median real wage is falling, by around 1% per year.
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Old 03-26-2012, 05:46 AM   #84
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See, this is why they shouldn't be yawning. Humans suck at estimating exponential rates of decay and compounding.

You made it easy by setting it up to drop in half (instead of double). I guesstimated the Rule of 72 (Rule of 72 - Wikipedia, the free encyclopedia) to come up with 7% because the rule works both ways. It turns out that the actual inflation rate is 7.17735%.

Juggling that Wikipedia formula gives you

r = exp[(ln2)/T] - 1 = exp[0.6931472/10 years] -1 = 0.0717735 per year.

In other words, you start with a buck and at the end of the first year you have 92.8 cents left. Do that nine more times and you only have 51 cents.

If inflation was 5% then at the end of the first year you'd have 95 cents. Doing it nine more times would leave 63 cents.

Getting it down to 50 cents would require about 14.4 years by the Rule of 72, although the actual number turns out to be about 14.206699 years.
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Thanks Nords, good catch.

I typed: ".....the prospect of moderate inflation causing the purchasing power of their non-COLA'd pension to drop by 50% over the next decade."

I was thinking: ".....the prospect of moderate inflation causing prices to increase by 50% over the next decade." That would have been the "moderate" inflation between 4% and 5% I mentioned.

My bad. And my apologies to you and the board participants.
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I calculate that after 10 iterations, you'd have 59.874 cents (0.95 ** 10, or 0.95 ^ 10 as the kids say these days ).

However, if inflation is defined as an increase in prices, then the corollary of 5% inflation is that after a year, $1 is worth not $0.95, but ($1 / 1.05) = 95.258 cents. Compound that nine further times (10 in total) and you end up with (0.95258 ** 10) = 61.391 cents.

You can check that by calculating (1.05 ** 10) = 1.62889 (that is, $1 invested at 5% compound with no deductions would give you $1.62889 after 10 years), and divide that into 1 => 1.0/1.62889 = 0.61391.
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Old 03-26-2012, 06:39 AM   #85
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I calculate that after 10 iterations, you'd have 59.874 cents (0.95 ** 10, or 0.95 ^ 10 as the kids say these days ).

However, if inflation is defined as an increase in prices, then the corollary of 5% inflation is that after a year, $1 is worth not $0.95, but ($1 / 1.05) = 95.258 cents. Compound that nine further times (10 in total) and you end up with (0.95258 ** 10) = 61.391 cents.

You can check that by calculating (1.05 ** 10) = 1.62889 (that is, $1 invested at 5% compound with no deductions would give you $1.62889 after 10 years), and divide that into 1 => 1.0/1.62889 = 0.61391.
First calc good for assessing deflation- cost of $1 worth merchandise costing 60 cents after 10 years of 5% deflation.
Second calc shows that with ten years of 5% inflation, $1 of merchandise will cost $1.63 (a 39% decline in purchasing power).
For example if beans went from $1 to $1.63 per kilo, you would get 387 grams less beans for $1 dollar at the $1.63 per kilo price.
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Old 03-26-2012, 07:10 AM   #86
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First calc good for assessing deflation- cost of $1 worth merchandise costing 60 cents after 10 years of 5% deflation.
Second calc shows that with ten years of 5% inflation, $1 of merchandise will cost $1.63 (a 61% decline in purchasing power).
Actually, the two calculations are essentially identical. The difference is that one shows a 38.609% drop in purchasing power (a dollar bill which has been filed under a mattress all that time used to buy you 1 pound of widgets, now it only buys you .61391 pounds of widgets), and the other shows a 62.889% increase in the cost of living (number of dollar bills needed to purchase a pound of widgets). That's why it's important to pay attention when people talk about percentage increases or decreases; the opposite of a 20% increase is not a 20% decrease.
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Old 03-26-2012, 07:27 AM   #87
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Agreed. I modified post # 85.
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Old 03-26-2012, 08:16 AM   #88
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Numbers is hard!

Just so you folks don't hurt your brains too much, here are some calcs I keep around for estimation/reality check purposes:

2.0% annual inflation over 10 years = 22% cumulative inflation
2.5% annual inflation over 10 years = 28% cumulative inflation
3.0% annual inflation over 10 years = 34% cumulative inflation
3.24% annual inflation over 10 years = 38% cumulative inflation

So you can see even "moderate" inflation like 3% means prices rise 34% over a decade. A huge hit to any wallet if your income hasn't grown with inflation.

And very "low" inflation - this is actually the minimum targeted by central banks because inflation rates below 2% usually means an economy is in trouble - still means prices rise by 22% over a decade. Ouch!

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Old 03-26-2012, 08:23 AM   #89
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Given the poll that shows were are mostly engineers, people can't figure out how to do this computation for themselves? Fer Chrissakes. Oh, I forgot, as REW's sig line says, math is hard... I found this illustration that proves it beyond a doubt!
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File Type: jpg MathIsHard.jpg (13.1 KB, 44 views)
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Old 03-26-2012, 08:30 AM   #90
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3.0% annual for 10 years = 34.392% cumulative.
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Old 03-26-2012, 08:36 AM   #91
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Central bankers, and many others, appear to want some inflation. And yes, when inflation runs away the central bankers can step and kill it. Collateral damage, however, can be pretty bad, and folks around here are likely casualties.
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I think there are only two levels of inflation: not enough or too much. We never have the one we want and overshoot when we reach for the one we don't have.
We agree on all of this.

Something else I should have included in my earlier comments, but didn't. I made it sound as if central bankers are sitting at a neutral position and can simply tighten as needed if inflation starts to pick up. But we know that isn't true today. There is a considerable unwind of accommodation that will eventually be needed to get the central bank back to neutral. It's possible, even likely, that uncertainty over the correct policy stance keeps the Fed behind the eight-ball for a time when inflation starts to pick up. I think it will be hard for the Fed to engineer a "Goldilocks" exit from it's current position and expect both higher than desirable intermediate inflation followed by a hard-ish landing. Collateral damage indeed.

But the common comparison to the 1970's I think is misplaced. We're not going back there unless the Fed loses its independence.
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Old 03-26-2012, 08:40 AM   #92
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3.0% annual for 10 years = 34.392% cumulative.
I guess I can't round! Fixed it. Thanks
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Old 03-26-2012, 08:42 AM   #93
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I guess I can't round! Fixed it. Thanks
Another example of what numbers is...
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Old 03-26-2012, 08:45 AM   #94
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Also, 3.24% inflation over 10 years is 39.0085%.... but really, when you are talking about 39% or 38%, one could skip the math and describe it as a whole %^(*& lot of inflation.
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Old 03-26-2012, 08:51 AM   #95
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Also, 3.24% inflation over 10 years is 39.0085%.... but really, when you are talking about 39% or 38%, one could skip the math and describe it as a whole %^(*& lot of inflation.
I got 37.56% W2R. I guess we have different numbers machines . I'm just doing a simple annual compounding over 10 years calculation.
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Old 03-26-2012, 08:53 AM   #96
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i got 37.56% w2r. I guess we have different numbers machines . I'm just doing a simple annual compounding over 10 years calculation.
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3.0% annual for 10 years = 34.392% cumulative.
1/((1-.03)^10)=1/(.97^10)=.34392
1/((1-.0324)^10)=1/(.9676^10)=.390085

Edited to add: dang, I thought this was how he was doing his.
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Old 03-26-2012, 09:14 AM   #97
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I'm doing (1+3.24%)^10 - 1 = .3756 That's how much prices went up.

The spreadsheet future value calculator gives me the same number for annual compounding over 10 years at a 3.24% rate.

and I get (1 + 3%)^10 - 1 = .34392 so I don't understand the discrepancy

Actually 1/((1-.03)^10) = 1.3561 so I think justplainbill used my method for cumulative inflation when he gave me the
34.392% number for 3% inflation.

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Old 03-26-2012, 09:15 AM   #98
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...a dollar bill which has been filed under a mattress all that time used to buy you 1 pound of widgets, now it only buys you .61391 pounds of widgets)...
Or it can be explained this way.

A $1 bill used to get you 1 lb of hamburger.

Now, it gets you 1 lb of pink slime.
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Old 03-26-2012, 09:15 AM   #99
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(1.03 ^ 10) -1 = .343916379......
(1.0324 ^ 10) -1 = .37556133....
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Old 03-26-2012, 09:17 AM   #100
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(1.03 ^ 10) -1 = .343916379......
(1.0324 ^ 10) -1 = .37556133....
+1

Or, a whole $%)(*& of a lot..
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