1. **Problem:** Calculate the compounded amount if Richard deposited 30000 at 8% interest compounded quarterly for 5 years. 2. **Formula:** The compound interest formula is $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount after time $t$ - $P$ is the principal (initial deposit) - $r$ is the annual interest rate (decimal) - $n$ is the number of times interest is compounded per year - $t$ is the time in years 3. **Given values:** - $P = 30000$ - $r = 0.08$ - $n = 4$ (quarterly) - $t = 5$ 4. **Calculation:** $$A = 30000 \left(1 + \frac{0.08}{4}\right)^{4 \times 5} = 30000 \left(1 + 0.02\right)^{20} = 30000 \times (1.02)^{20}$$ 5. Calculate $(1.02)^{20}$: $$ (1.02)^{20} \approx 1.485947 $$ 6. Multiply by principal: $$ A = 30000 \times 1.485947 = 44578.41 $$ 7. **Answer:** The compounded amount after 5 years is approximately Php 44578.42. This matches the option Php 44,578.42.