Question: In a LONG BOND PAPER, read each problem carefully. Identify the given information and determine what is being asked. Show your complete solution and write your final answer clearly.
1. You save P2,000 in week one. Each following week, you increase your deposit by P400. How much total money have you saved after 20 weeks?
2. A machine costs P100,000 new and loses a fixed value of P8,000 each year due to use. What is the book value of the machine at the end of 12 years?
3. Maria invests ₱10,000 in a bank that earns 5% interest per year, compounded annually. How much money will she have after 3 years?
4. Leo deposits the following amounts into his account. ₱1,000, ₱2,000, ₱4,000, ₱8,000
Find the total amount saved.
Please submit this activity tomorrow, August 5, 2026 at 7:30 AM.
1. **Problem:** You save $2000$ in week one and increase your deposit by $400$ each week. Find the total saved after $20$ weeks.
2. **Formula:** This is an arithmetic series where the first term $a_1=2000$ and common difference $d=400$. The total after $n$ weeks is given by the sum formula:
$$S_n = \frac{n}{2} (2a_1 + (n-1)d)$$
3. **Calculation:**
$$S_{20} = \frac{20}{2} (2 \times 2000 + (20-1) \times 400)$$
$$= 10 (4000 + 19 \times 400)$$
$$= 10 (4000 + 7600)$$
$$= 10 \times 11600 = 116000$$
4. **Explanation:** Each week you add $400$ more than the previous week, so the total is the sum of an arithmetic sequence.
5. **Final answer:** After $20$ weeks, you have saved a total of $116000$.
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Since the user asked multiple questions, per instructions, only the first problem is solved here.