With the somewhat generous annual interest of 6%, it would be around $1000. Not exactly back breaking for the DoD (or the VA, for that matter, whatever department has this issue on their table).

You're off by a factor of ten. Assuming monthly compounding:

(1 + .06/12)^(12 * (2017-1944)) = 78.97

78.97 * 180 = 14214

However the final amount is highly sensitive to interest rate assumed, for different interest rates:

.02 774.13

.04 3,321.26

.06 14,214.86

.08 60,692.55

.10 258,514.77

.12 1,098,489.57

However it's unlikely that the money would have been invested anyways.

You are wrongly calculating with $180 instead of $13. The $180 figure is $13 adjusted by inflation.

While true using 6% during periods where inflation was > 6% is a poor interest rate. IMO, inflation +4% is reasonable.

Can't include both interest and inflation. It's one or the other, not both.

You can certainly include both interest and inflation.

no, it's double counting. Assume he had objected at the time and the money was put away during his appeal. It would accumulate interest until the appeal was settled, it doesn't accumulate inflation. Inflation is the measure of how each dollars buying power lessens over time.

No you can't the compounding interest would be one the money actually in the bank at each point in time not what it is nominally worth adjusting for changes in purchasing power. For example if I deposited money today and earned 5% interest what happens to the values of that money due to inflation doesn't matter (baring some intervention).

How so?

Say you put £100 in the bank 50 years ago.

Compound interest tells us how much money we have. If we assume an improbably static 2% every year, today we have ~£270 in our account.

Inflation doesn't work on top of that because £270 is what it's already worth today. Inflation tells us what our original £100 is worth in terms of buying power.

If a loaf of bread cost £0.10 in 1967 but costs £1.50 today, we can say over 50 years there has been 150% inflation. These sorts of price index comparisons allow us to compare worth back then.

Or in reverse, you can see this in very real terms. You could look at your £270 and see that would only buy you 180 loaves of bread. In 1967, your £100 would have garnered 1000 loaves. Interest has not kept up with inflation. You have lost money —in this example— by "saving" it.

On a shorter timescale, RPI and CPI allow central banks to see inflation and —to a point— alter their base rates to help influence the balance of savers-vs-spenders, lessening the popular disposable cash, and lessening inflation.

That's the theory, anyway.

Though obviously I skwonked the percentage increase there. The inflation in that tiny bread example was 1400%

You've just defined the real interest rate, as opposed to the nominal rate

No

He might have spent the money in ways that later benefited him - even if he bought a house that was 13$ more expensive, given the housing boom during his lifetime in many locations he would have made more than a 6% return. You're never going to be able to really figure that what-if game anyhow... I think interest is an appropriate simplification (certainly more appropriate than inflation).