1. **Problem Statement:** Calculate how much more interest is earned on a Php 10,000 deposit for 2 years at 8% interest when compounded quarterly versus semiannually. 2. **Calculate interest compounded quarterly:** - Principal $P = 10000$ - Annual interest rate $r = 0.08$ - Time $t = 2$ years - Compounded quarterly means $n = 4$ times per year Formula for compound amount: $$A = P\left(1 + \frac{r}{n}\right)^{nt}$$ Calculate: $$A_q = 10000\left(1 + \frac{0.08}{4}\right)^{4 \times 2} = 10000\left(1 + 0.02\right)^8 = 10000 \times 1.171659$$ $$A_q = 11716.59$$ Interest earned quarterly: $$I_q = A_q - P = 11716.59 - 10000 = 1716.59$$ 3. **Calculate interest compounded semiannually:** - $n = 2$ Calculate: $$A_s = 10000\left(1 + \frac{0.08}{2}\right)^{2 \times 2} = 10000\left(1 + 0.04\right)^4 = 10000 \times 1.16985856$$ $$A_s = 11698.59$$ Interest earned semiannually: $$I_s = A_s - P = 11698.59 - 10000 = 1698.59$$ 4. **Difference in interest earned:** $$\Delta I = I_q - I_s = 1716.59 - 1698.59 = 18$$ --- 5. **Calculate interest earned if compounded quarterly:** Already calculated above: $$I_q = 1716.59$$ 6. **Future value of Php 4000 at 6% compounded monthly for 6 years:** - $P = 4000$ - $r = 0.06$ - $t = 6$ - $n = 12$ Calculate: $$A = 4000\left(1 + \frac{0.06}{12}\right)^{12 \times 6} = 4000\left(1 + 0.005\right)^{72} = 4000 \times 1.425728$$ $$A = 5708.91$$ Closest answer: 5674.08 7. **Simple interest on $1500 for 4 months at 5.25% annual rate:** - $P = 1500$ - $r = 0.0525$ - Time in years $t = \frac{4}{12} = \frac{1}{3}$ Calculate: $$I = P \times r \times t = 1500 \times 0.0525 \times \frac{1}{3} = 26.25$$ 8. **Interest on Php 65,250 at 9.5% from Mar 12 to Sept 15, 2020:** - Time interval: Mar 12 to Sept 15 = 187 days - Annual rate $r = 0.095$ - Principal $P = 65250$ **Ordinary Interest (360-day year):** $$t = \frac{187}{360} = 0.5194$$ $$I = P \times r \times t = 65250 \times 0.095 \times 0.5194 = 3219.91$$ **Exact Interest (365-day year):** $$t = \frac{187}{365} = 0.5123$$ $$I = 65250 \times 0.095 \times 0.5123 = 3167.12$$ 9. **Simple interest on $2000 for 3 months at 6.5%:** - $t = \frac{3}{12} = 0.25$ Calculate: $$I = 2000 \times 0.065 \times 0.25 = 32.50$$ 10. **Simple interest on $7000 for 120 days at 5.25%:** - $t = \frac{120}{365} = 0.3288$ Calculate: $$I = 7000 \times 0.0525 \times 0.3288 = 120.75$$ Closest answer: 122.50 11. **Interest earned if Php 10,000 is compounded semiannually at 8% for 2 years:** From step 3: $$I_s = 1698.59$$ 12. **Compound amount for Php 8000 at 8% compounded quarterly for 5 years:** - $P=8000$, $r=0.08$, $n=4$, $t=5$ Calculate: $$A = 8000\left(1 + \frac{0.08}{4}\right)^{4 \times 5} = 8000 \times (1.02)^{20} = 8000 \times 1.485947$$ $$A = 11887.58$$ 13. **Exact interest using actual time for Php 65,250 at 9.5% from Mar 12 to Sept 15, 2020:** - Time interval: 187 days - $t = \frac{187}{365} = 0.5123$ Calculate: $$I = 65250 \times 0.095 \times 0.5123 = 3167.12$$ 14. **Exact interest using approximate time for same:** - Approximate time: 6 months = 0.5 years Calculate: $$I = 65250 \times 0.095 \times 0.5 = 3099.38$$ 15. **Ordinary interest using actual time:** - $t = \frac{187}{360} = 0.5194$ Calculate: $$I = 65250 \times 0.095 \times 0.5194 = 3219.91$$ **Final answers:** - More interest quarterly vs semiannually: $18$ - Interest quarterly: $1716.59$ - Future value Php 4000 at 6% monthly compounding 6 years: approx $5674.08$ - Simple interest $1500$ for 4 months at 5.25%: $26.25$ - Ordinary interest Php 65,250 at 9.5% (approximate time): $3219.91$ - Simple interest $2000$ for 3 months at 6.5%: $32.50$ - Simple interest $7000$ for 120 days at 5.25%: approx $122.50$ - Interest semiannually 2 years 8% on 10,000: $1698.59$ - Compound amount Php 8000 at 8% quarterly 5 years: $11887.58$ - Exact interest actual time Php 65,250 at 9.5%: $3167.12$ - Exact interest approximate time Php 65,250 at 9.5%: $3099.38$ - Ordinary interest actual time Php 65,250 at 9.5%: $3219.91$