1. **Problem 1:** Find the present value of 80000 due in 2 years at 12% interest compounded quarterly. 2. The formula for present value with compound interest is: $$PV = \frac{FV}{\left(1 + \frac{r}{n}\right)^{nt}}$$ where $PV$ is present value, $FV$ is future value, $r$ is annual interest rate (decimal), $n$ is number of compounding periods per year, and $t$ is time in years. 3. For problem 1, $FV=80000$, $r=0.12$, $n=4$ (quarterly), $t=2$. 4. Calculate the denominator: $$1 + \frac{0.12}{4} = 1 + 0.03 = 1.03$$ 5. Calculate the exponent: $$nt = 4 \times 2 = 8$$ 6. Calculate the present value: $$PV = \frac{80000}{1.03^8} = \frac{80000}{1.26677} \approx 63157.32$$ 7. **Answer for problem 1:** ₱63157.32 --- 8. **Problem 2:** Find the compound interest from problem 1. 9. Compound interest is the difference between future value and present value: $$CI = FV - PV = 80000 - 63157.32 = 16842.68$$ 10. **Answer for problem 2:** ₱16842.68 --- 11. **Problem 3:** Find the present value of 20000 due in 5 years at 12% interest compounded semi-annually. 12. Here, $FV=20000$, $r=0.12$, $n=2$ (semi-annually), $t=5$. 13. Calculate the denominator: $$1 + \frac{0.12}{2} = 1 + 0.06 = 1.06$$ 14. Calculate the exponent: $$nt = 2 \times 5 = 10$$ 15. Calculate the present value: $$PV = \frac{20000}{1.06^{10}} = \frac{20000}{1.79085} \approx 12844.01$$ 16. **Answer for problem 3:** ₱12844.01