1. **State the problem:** We want to find how long it will take for ₱12,000 to earn ₱3,600 in interest at a 10% simple interest rate. 2. **Formula for simple interest:** $$I = P \times r \times t$$ where $I$ is the interest earned, $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. 3. **Identify known values:** - $I = 3600$ - $P = 12000$ - $r = 10\% = 0.10$ 4. **Substitute values into the formula:** $$3600 = 12000 \times 0.10 \times t$$ 5. **Simplify the right side:** $$3600 = 1200 \times t$$ 6. **Solve for $t$ by dividing both sides by 1200:** $$t = \frac{3600}{1200}$$ 7. **Show cancellation:** $$t = \frac{\cancel{3600}}{\cancel{1200}} = 3$$ 8. **Final answer:** It will take **3 years** for ₱12,000 to earn ₱3,600 at 10% simple interest.