1. **State the problem:** Calculate the nominal interest rate $j$ compounded daily for a credit card balance. 2. **List variables and given values:** - Present Value (PV) = 1850 - Future Value (FV) = 1845.77 + 35 = 1880.77 (adding back the payment) - Number of compounding periods per year $m = 365$ - Time in years $t = \frac{31}{365}$ - Number of compounding periods $n = m \times t = 365 \times \frac{31}{365} = 31$ 3. **Formula used:** $$FV = PV(1 + j)^n$$ where $j$ is the nominal interest rate per compounding period. 4. **Solve for $j$:** $$1880.77 = 1850(1 + j)^{31}$$ Divide both sides by 1850: $$\frac{1880.77}{1850} = (1 + j)^{31}$$ $$1.016632432 = (1 + j)^{31}$$ Take the 31st root: $$1.016632432^{\frac{1}{31}} = 1 + j$$ Calculate: $$1.000532259 = 1 + j$$ Subtract 1: $$j = 1.000532259 - 1 = 0.000532259$$ 5. **Calculate nominal annual interest rate $i$:** $$i = j \times m = 0.000532259 \times 365 = 0.194274405$$ Convert to percentage: $$i = 0.194274405 \times 100 = 19.43\%$$ 6. **Concluding statement:** The nominal interest rate compounded daily is approximately **19.43%** per year, rounded to two decimal places.