This study introduces a central bank digital currency (CBDC) – both interest-bearing and non-interest-bearing – into a standard New Keynesian dynamic stochastic general equilibrium (DSGE) model à la Smets and Wouters (2007), and analyzes the effects of a CBDC on the transmission channel of monetary policy. In contrast to New Monetarist approaches, a DSGE-based model enables us to examine the qualitative and quantitative implications of monetary policy in the short run, as well as in the long run. The CBDC, defined as an imperfect substitute for cash and demand deposits, affects the optimal decision of households and private banks through the interest rate channel, as well as the credit channel. In line with the existing literature, a non-interest-bearing CBDC may partially replace demand deposits and lead to an increase in bank financing costs and loan interest rates. This, in turn, induces asymmetric effects on the deposit and loan rates and may reduce the loan amount, thus investment. These asymmetric – and thereby real – effects are found to be larger the more competitive the bank industry is. Our calibration analysis using Korean data, however, reveals that the quantitative effects on the investment and output are found to be very small, even in the case of monopoly in the bank industry both in the long run and in the short run. Meanwhile, the analysis shows that the effects of the policy rate on the economy after the introduction of a non-interest-bearing CBDC will not be much different from before its introduction. Finally, assuming that an interest-bearing CBDC is introduced, we find that the CBDC interest rate can function as an additional policy instrument independent of the main policy rate. Moreover, the interest payment on a CBDC may raise the deposit rate more than the loan rate, possibly lowering the real lending rate. Henceforth, it may actually encourage investment, leading to higher output. Nevertheless, we find that the quantitative effects are still quite small relative to the findings documented in the literature.