1. **State the problem:** We need to find the principal amount that will earn 176.42 in interest at an annual simple interest rate of 4.75% over 8 months. 2. **Formula for simple interest:** $$I = P \times r \times t$$ where $I$ is the interest earned, $P$ is the principal, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. 3. **Convert given values:** - Interest $I = 176.42$ - Rate $r = 4.75\% = 0.0475$ - Time $t = \frac{8}{12} = \frac{2}{3}$ years 4. **Rearrange formula to find principal:** $$P = \frac{I}{r \times t}$$ 5. **Substitute values:** $$P = \frac{176.42}{0.0475 \times \frac{2}{3}} = \frac{176.42}{0.0316667}$$ 6. **Calculate principal:** $$P \approx 5568.94$$ **Answer:** The principal amount is approximately 5568.94.