Is this a legitimate way to consider a lending policy under a zero interest or negative interest rate banking?
Two-Pool Demurrage Bond Model
Setup
A lender deposits principal P_0 into a term contract. Over time, two balances evolve:
· Principal pool P_t – depreciates at rate d per period (the demurrage / holding tax).
· Return pool R_t – accumulates returns, then also depreciates at rate d.
The return is calculated on the combined total (P_t + R_t), added to R_t, and only then does the depreciation hit both pools.
Period‑by‑period dynamics
```
P_t = (1-d) * P_{t-1}
R_t = (1-d) * [ R_{t-1} + r * (P_{t-1} + R_{t-1}) ]
```
Where:
· P_0 = initial principal
· d = demurrage rate (e.g. 0.03 for 3%)
· r = nominal return rate applied to the total balance (P + R)
· t = time in periods (e.g. years)
Closed‑form solution
Because P_t = P_0 * (1-d)^t, the return pool has a tidy closed form:
R_t = P_0 * (1-d)^t * [ (1+r)^t – 1 ]
And the total value:
V_t = P_t + R_t = P_0 * [ (1-d)(1+r) ]^t
Key properties economists will spot immediately
Property Formula
Breakeven return rate r* = d / (1-d)
Effective CAGR g = (1-d)(1+r) – 1 = r – d – r*d
Principal share of total P_t / V_t = (1+r)^{-t}
Return pool share of total R_t / V_t = 1 – (1+r)^{-t}
At maturity (when P_t → 0), the lender essentially receives R_t.
Numerical example
Parameter Value
Principal P_0 $1,000
Demurrage d 3% per year
Nominal return r 5% per year
Term T 33 years
Results:
· P_33 = $366
· R_33 = $1,465
· Maturity payout = $1,831 (1.83× principal)
· Effective CAGR = 1.85% per year
If r = 3.093%, the payout equals exactly $1,000 (breakeven). Any r below that means the lender loses nominal principal.
One‑line framing
"This is a zero-interest lending policy where the demurrage tax applies to both principal and reinvested returns, but returns are calculated on the growing total balance. It forces money into circulation while allowing lenders to preserve purchasing power through a compounded return pool that replaces the depreciated principal at maturity