1. **State the problem:** On June 1, after making a minimum payment of 35, the new balance was 1845.77. We need to find the nominal interest rate compounded daily given the initial purchase was 1850 on May 1. 2. **Understand the situation:** Interest is compounded daily on the remaining balance after payment. 3. **Set up the compound interest formula:** $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount after interest, - $P$ is the principal after payment, - $r$ is the nominal annual interest rate (to find), - $n=365$ (daily compounding), - $t$ is time in years. 4. **Calculate principal after payment:** $$P = 1850 - 35 = 1815$$ 5. **Calculate time $t$ in years:** From May 1 to June 1 is 31 days, $$t = \frac{31}{365}$$ 6. **Plug values into 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:** $$r = 19.71\%$$ **Final answer:** The nominal interest rate compounded daily is **19.71\%**.