1. **State the problem:** Juliana invested 3450 at 5.25% per annum simple interest. We need to find how many days it takes for the investment to grow to 3580. 2. **Formula for simple interest:** $$A = P + I = P + P \times r \times t$$ where $A$ is the amount after time $t$, $P$ is the principal, $r$ is the annual interest rate (in decimal), and $t$ is time in years. 3. **Calculate the interest earned:** $$I = A - P = 3580 - 3450 = 130$$ 4. **Use the simple interest formula to find $t$:** $$I = P \times r \times t$$ $$130 = 3450 \times 0.0525 \times t$$ 5. **Solve for $t$:** $$t = \frac{130}{3450 \times 0.0525}$$ $$t = \frac{130}{180.125}$$ 6. **Simplify the fraction:** $$t = \frac{\cancel{130}}{\cancel{180.125}} \approx 0.7217 \text{ years}$$ 7. **Convert years to days:** $$t = 0.7217 \times 365 = 263.32 \text{ days}$$ 8. **Round up to the next day:** $$\boxed{264 \text{ days}}$$ So, it will take 264 days for Juliana's investment to grow to 3580 with simple interest at 5.25% p.a.