We build a tractable small-open-economy Dynamic Stochastic General Equilibrium (DSGE) model with monopolistically competitive banks to study the macro-financial effects of introducing a sovereign digital currency (SDC) - here modeled as an account-based central bank digital currency (CBDC). Households choose between bank deposits and SDC holdings; banks finance loans largely with deposits and face a reduced-form intermediation capacity. Mechanism — higher attractiveness of an interest-bearing SDC mechanically substitutes away bank deposits, reducing bank funding and, absent recycling, shrinking loan supply and lowering aggregate credit. Quantitatively, under our baseline calibration a 10% reallocation from bank deposits into SDC implies an≈3.2% contraction in bank lending and a consumption-equivalent welfare loss of ≈0.039% (worst-case scenarios reach ≈8.0% welfare loss when recycling is absent and intermediation is fragile). Policy experiments show that (i) modest or tiered remuneration on SDC, (ii) limits/tiering on holdings, and (iii) active central-bank recycling of inflows into bank funding substantially mitigate credit and welfare losses. Our results are robust across parameter sweeps. Policy implication — combining tiered remuneration with credible recycling is the most effective way to preserve credit while delivering the liquidity and payment-system benefits of SDC. Limitations — the analysis is theoretical, uses a reduced-form banking block and illustrative calibration; country-level empirical calibration and endogenous bank-risk dynamics are left for future work.