You're completely missing the point. The Fed did a fantastic job, because they could have given a pretty good estimate of that number in 1914. If you had asked someone in 1814 what a dollar would be worth in 1914, hell, 1824, they would have been guessing, and been wildly wrong.
Making sure that the nitwits stuffing their mattresses with dollar bills maintain their net worth is not the goal of our monetary policy, nor is a good goal. The goal is to ensure predictability.
To this end, we can model the price level at some point in time in a way similar to how we model compounding interest: P(t) = P(0) * (1.0 + r)^t. Take P(0) = 1.0, r = 0.032, and t = 2026-1914 = 112. Then, P(112) = 1.0 * (1.032)^112 = 34.05. We've had an average 3.2% rate of inflation in the price level over the past 112 years, give or take.
We can make certain assumptions that the rate of inflation won't be far off from this when we evaluate certain financial risks.
Just as in modeling adjustable interest rates for compounding interest, we can make r depend on t, and at that point, it becomes an ODE problem: dP/dt = r(t) * P(t).
This betrays a lack of understanding of nominal versus real debt dynamics. (And also taxes, but I'll admit that my upbringing has probably given me a unique perspective on Caesar and what it means for us to be able to use his money.)
Of particular note, debt instruments are denominated in nominal dollars, and they're paid back in nominal dollars, but what concerns the creditor is the real value of those nominal payments. Economic growth has this pernicious habit of pushing nominal prices upward, and if the money supply and credit system don't grow commensurate with the resulting increased demand for liquidity, the real burden of existing nominal debts can rise sharply and unpredictably.
This means that borrowers can find themselves underwater on, e.g., mortgages while the nominal obligations remain fixed, and banks will swiftly foreclose on them and tighten credit when considering their balance sheets. Many of the panics of the 1800's included a lot of this very dynamic.
A 1914 dollar is worth $33 today. Great job, Fed!