1. **Problem Statement:** Gary deposits 3579.72 at the beginning of every month for 5 years. The fund is compounded quarterly at an annual interest rate of 3.5%. We need to find the value of $i_2$, which is the interest rate per quarter. 2. **Understanding the problem:** The annual nominal interest rate is 3.5%, compounded quarterly. This means the interest rate is divided into 4 quarters per year. 3. **Formula:** The interest rate per quarter $i_2$ is given by dividing the annual nominal rate by the number of compounding periods per year: $$i_2 = \frac{r}{m}$$ where: - $r = 0.035$ (annual nominal rate as a decimal) - $m = 4$ (number of compounding periods per year) 4. **Calculation:** $$i_2 = \frac{0.035}{4} = 0.00875$$ 5. **Rounding:** The problem asks to round to 6 decimal places: $$i_2 = 0.008750$$ 6. **Interpretation:** The quarterly interest rate $i_2$ is 0.008750 or 0.875%. This is the interest rate applied every quarter for compounding. **Final answer:** $$\boxed{i_2 = 0.008750}$$