1. **State the problem:** Joe deposits 10 initially and 10 more at the start of each month into a bank account paying 2% compound interest monthly. We want to find the compound interest earned on the original 10 after 2 years (24 months). 2. **Formula for compound interest:** The amount after $n$ months with monthly compound interest rate $r$ on principal $P$ is $$A = P(1+r)^n$$ 3. **Apply values:** Here, $P=10$, $r=0.02$, $n=24$. 4. **Calculate total amount from original 10:** $$A = 10(1+0.02)^{24} = 10(1.02)^{24}$$ 5. **Calculate compound interest earned:** Compound interest = Total amount - Principal = $$10(1.02)^{24} - 10$$ 6. **Evaluate:** Calculate $(1.02)^{24}$ using a calculator or approximation. 7. **Final answer:** Compound interest earned on original 10 after 2 years is $$10((1.02)^{24} - 1)$$. This completes the solution for question 7 (i).