1. **State the problem:** You invest 10,000 dollars with 3% interest compounded yearly for 3 years, then 6% interest compounded yearly for 2 more years. Find the amount after 5 years. 2. **Formula for compound interest:** $$A = P \times (1 + r)^t$$ where $A$ is the amount, $P$ is the principal, $r$ is the annual interest rate (as a decimal), and $t$ is the time in years. 3. **Apply the formula in two stages:** - For the first 3 years at 3%: $$A_3 = 10000 \times (1 + 0.03)^3$$ - For the next 2 years at 6%, the amount $A_3$ becomes the new principal: $$A_5 = A_3 \times (1 + 0.06)^2$$ 4. **Write the full expression:** $$A_5 = 10000 \times (1 + 0.03)^3 \times (1 + 0.06)^2$$ This expression represents the total amount after 5 years with the given interest rates and compounding periods.