1. **State the problem:** Alana made a purchase of 1850 on May 01. On June 01, after making a minimum payment of 35, her new balance was 1845.77. We need to find the nominal interest rate compounded daily. 2. **Understand the situation:** The interest is charged daily on the remaining balance from the date of purchase if the full balance is not paid. 3. **Set up the formula:** The balance after interest is calculated by compound interest formula: $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount after interest, - $P$ is the principal (initial balance after payment), - $r$ is the nominal annual interest rate (to find), - $n$ is the number of compounding periods per year (daily compounding means $n=365$), - $t$ is the time in years. 4. **Calculate the principal after payment:** Initial balance: 1850 Payment: 35 Remaining principal after payment: $$P = 1850 - 35 = 1815$$ 5. **Calculate time $t$:** From May 01 to June 01 is 31 days. Convert to years: $$t = \frac{31}{365}$$ 6. **Plug values into the formula and solve for $r$:** $$1845.77 = 1815 \left(1 + \frac{r}{365}\right)^{31}$$ Divide both sides by 1815: $$\frac{1845.77}{1815} = \left(1 + \frac{r}{365}\right)^{31}$$ $$1.0169 = \left(1 + \frac{r}{365}\right)^{31}$$ 7. **Take the 31st root:** $$\left(1.0169\right)^{\frac{1}{31}} = 1 + \frac{r}{365}$$ Calculate left side: $$1.00054 = 1 + \frac{r}{365}$$ 8. **Solve for $r$:** $$\frac{r}{365} = 1.00054 - 1 = 0.00054$$ Multiply both sides by 365: $$r = 0.00054 \times 365 = 0.1971$$ 9. **Convert to percentage and round:** $$r = 19.71\%$$ **Final answer:** The nominal interest rate compounded daily is **19.71\%**.