1. **State the problem:** Rhianna invests ₱50000 and wants it to grow to ₱65000 in 4 years with interest compounded semiannually. 2. **Identify known values:** - Principal, $P = 50000$ - Amount, $A = 65000$ - Time, $t = 4$ years - Compounding periods per year, $n = 2$ - We want to find the annual interest rate $r$ compounded semiannually. 3. **Formula for compound interest:** $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ 4. **Substitute known values:** $$65000 = 50000 \left(1 + \frac{r}{2}\right)^{2 \times 4} = 50000 \left(1 + \frac{r}{2}\right)^{8}$$ 5. **Divide both sides by 50000:** $$\frac{65000}{50000} = \left(1 + \frac{r}{2}\right)^8$$ $$1.3 = \left(1 + \frac{r}{2}\right)^8$$ 6. **Take the 8th root of both sides:** $$1 + \frac{r}{2} = (1.3)^{\frac{1}{8}}$$ 7. **Calculate $(1.3)^{1/8}$:** $$ (1.3)^{\frac{1}{8}} \approx 1.03368$$ 8. **Solve for $r$:** $$1 + \frac{r}{2} = 1.03368$$ $$\frac{r}{2} = 1.03368 - 1 = 0.03368$$ $$r = 2 \times 0.03368 = 0.06736$$ 9. **Convert to percentage:** $$r = 6.736\%$$ 10. **Answer:** Rhianna should invest her money at approximately **6.74%** compounded semiannually to reach ₱65000 in 4 years. Among the options given, the closest is **6.68%**.