A bank can lend R$25,000.00 at an effective interest rate of 42% per year or use this capital in compound rational discount operations with a term of 90 days. What should be the monthly discount rate applied to a R$20,000.00 invoice, so that the bank has an effective return equal to that obtained on the loan?

1. Annual effective interest rate:
i_{eff} = 0.42
2. Annual effective discount rate:
d_{eff} = \frac{i_{eff}}{1 + i_{eff}} = \frac{0.42}{1 + 0.42} = \frac{0.42}{1.42} \approx 0.2958

3. Convert annual effective discount rate to a quarterly effective discount rate (for 90 days):
1 - d_{q} = (1 - d_{eff})^{1/4}
1 - d_{q} = (1 - 0.2958)^{1/4} \approx 0.9407
d_{q} = 1 - 0.9407 \approx 0.0593

4. Convert the quarterly discount rate to a monthly discount rate:
1 - d_{m} = (1 - d_{q})^{1/3}
1 - d_{m} = (1 - 0.0593)^{1/3} \approx 0.9698
d_{m} = 1 - 0.9698 \approx 0.0302

5. Adjust for a compounded situation where the monthly rate is equivalent to achieve the effective return:
(1-0.0302)^{12} \approx 0.632
d_{annual} = 1 - 0.632 \approx 0.368
(1 + r_{m})^{12} - 1 = 0.42
r_{m} \approx 1.42^{1/12} - 1 \approx 0.0293

Therefore, the monthly discount rate applied is approximately:

r = 0.06 \, \text{(or 6%)}