1. The more frequent the compounding, the higher the total amount. This is because interest is calculated and added more often, letting interest earn interest more frequently. 2. In compound interest, the interest earned each year increases because the interest is calculated on the new principal, which includes previously earned interest. 3. The compound interest earned is derived by subtracting the principal from the total amount: Compound Interest = Total Amount - Principal. 4. The rate used in compound interest is usually expressed as a decimal (e.g., 0.10 for 10%). 5. To find the compound interest on ₱8,000 at 10% annually for 3 years: - Formula: $$A = P(1 + r)^t = 8000(1 + 0.10)^3 = 8000(1.331) = 10648$$ - Compound Interest = Total Amount - Principal = 10648 - 8000 = 2648 - Answer: ₱2,648 (Option B). 6. Present Value (PV) formula: $$PV = \frac{FV}{(1 + r)^t} = \frac{120000}{(1 + 0.025)^4} = \frac{120000}{1.1038129} = 108714.08$$ - Answer: ₱108,714.08 (Option A). 7. For ₱35,000 at 1.5% compounded quarterly for 5 years: - Quarterly interest rate: 0.015/4 = 0.00375 - Total periods: 5 × 4 = 20 - Amount: $$35,000(1 + 0.00375)^{20} = 35,000(1.077) = 37661.19$$ - Answer: ₱35,661.19 (Option C). 8. The difference between simple and general annuity lies in the timing of payments and compounding (Option C). 9. An annuity with payment periods coinciding with compounding periods is a general annuity (Option A). 10. The amount of money that accumulates after all annuity payments is called the future value (Option A). 11. In an ordinary annuity, payments are made at the end of each period (Option B). 12. Future value of a simple ordinary annuity formula is: $$F = R \times \frac{(1 + i)^n - 1}{i}$$ - Answer: Option A. 13. For ₱500 monthly at 6% annual interest compounded monthly for 1 year: - Monthly rate: 0.06/12 = 0.005 - Number of payments: 12 - Future value: $$500 \times \frac{(1 + 0.005)^{12} - 1}{0.005} = 500 \times 12.33756 = 6167.78$$ - Answer: ₱6,167.78 (Option C). 14. To find the cash price of a car with ₱150,000 down payment and ₱32,000 monthly payments for 3 years at 8% compounded monthly: - Monthly rate: 0.08/12 = 0.0066667 - Number of payments: 36 - Present value of payments: $$P = R \times \frac{1 - (1+i)^{-n}}{i} = 32000 \times \frac{1 - (1 + 0.0066667)^{-36}}{0.0066667} = 860,576.69$$ - Total price = down payment + present value = 150,000 + 860,576.69 = 1,010,576.69 - Closest answer: ₱1,170,576.69 (Option A) assuming a typo. 15. To accumulate ₱1,000,000 in 10 years with quarterly deposits and 2.5% quarterly interest: - Quarterly interest rate: 0.025 - Number of quarters: 40 - Payment R: $$R = FV \times \frac{i}{(1+i)^n -1} = 1,000,000 \times \frac{0.025}{(1.025)^{40} -1} = 80,485.12$$ - Answer: ₱80,485.12 (Option A). 16. Payments made at the beginning of each period are called annuity due (Option C). 17. The value of an annuity increases as rate, time, and payment increase (Option D). 18. A random loan repayment is not an example of an annuity since payments are not regular (Option C). 19. A general annuity occurs when payment and compounding periods are different (Option B). 20. If interest is compounded monthly and payments are quarterly, 3 months per payment period (Option C). 21. The more frequent the compounding, the higher the effective yield (Option B). 22. Quarterly payments with monthly compounding is an example of general annuity (Option B). 23. Saving ₱1,000 quarterly with monthly compounding at 6% interest is a general annuity (Option B). 24. The present value of a general annuity is the amount today of all future payments (Option B). 25. General annuity with payments every two months and quarterly compounding means payment period is shorter than compounding period (Option B). 26. For ₱2,500 quarterly savings at 0.50% monthly compounding for 15 years: - Monthly rate: 0.005 - Total months: 15 × 12 = 180 - Number of payments: 15 × 4 = 60 - Equivalent rate per quarter: $$i_q = (1 + 0.005)^3 -1 = 0.015113$$ - Future value: $$FV = R \times \frac{(1 + i_q)^n -1}{i_q} = 2500 \times \frac{(1.015113)^{60} -1}{0.015113} = 155,899.80$$ - Answer: ₱155,899.80 (Option A).