1. **Problem Statement:** Gary deposits 2366.3 every 2 months for 4 years, with the fund compounded semi-annually at 8.1%. We need to find the value of the interest rate per compounding period, denoted as $i_2$, rounded to 6 decimal places. 2. **Understanding the problem:** The nominal annual interest rate is 8.1%, compounded semi-annually. This means the interest is compounded twice a year. 3. **Formula for interest rate per compounding period:** $$i_2 = \frac{r}{m}$$ where $r$ is the nominal annual interest rate (as a decimal), and $m$ is the number of compounding periods per year. 4. **Given values:** - $r = 8.1\% = 0.081$ - $m = 2$ (since semi-annual compounding) 5. **Calculate $i_2$:** $$i_2 = \frac{0.081}{2} = 0.0405$$ 6. **Rounding to 6 decimal places:** $$i_2 = 0.040500$$ 7. **Interpretation:** The interest rate per semi-annual period is 0.040500 or 4.05%.