1. **State the problem:** We need to find the value of $P_g$ using the formula: $$P_g = A_1 \frac{1 - \left(\frac{1+g}{1+i}\right)^n}{i - g}$$ where $g=0.07$, $i=0.12$, $A_1=1000$, and $n=10$. 2. **Substitute the values into the formula:** $$P_g = 1000 \times \frac{1 - \left(\frac{1+0.07}{1+0.12}\right)^{10}}{0.12 - 0.07}$$ 3. **Calculate the fraction inside the power:** $$\frac{1+0.07}{1+0.12} = \frac{1.07}{1.12} \approx 0.955357$$ 4. **Raise this value to the power of $n=10$:** $$0.955357^{10} \approx 0.6376$$ 5. **Calculate the numerator:** $$1 - 0.6376 = 0.3624$$ 6. **Calculate the denominator:** $$0.12 - 0.07 = 0.05$$ 7. **Calculate $P_g$:** $$P_g = 1000 \times \frac{0.3624}{0.05} = 1000 \times 7.248 = 7248$$ **Final answer:** $$P_g \approx 7248$$