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Let's break down the problem step by step:

### Given Data:
- **Initial Down Payment**: ₱1,000,000
- **Quarterly Payment**: ₱250,000 for 5 years
- **Interest Rate**: 5% compounded annually

### Steps to Determine Economic Value:
1. **Initial Down Payment**: This amount is already paid upfront, so its present value is ₱1,000,000.

2. **Quarterly Payments**: These payments occur every quarter for 5 years, making it 20 payments in total. The present value of these payments is calculated using the formula for the present value of an annuity, adjusted for quarterly compounding.

   Since the 5% interest is compounded annually but payments are quarterly, we need to adjust the interest rate to match the quarterly period:
   \[
   i_{quarterly} = \frac{5\%}{4} = 0.0125
   \]
   The number of quarters in 5 years:
   \[
   n = 5 \times 4 = 20
   \]
   Using the present value of an annuity formula:
   \[
   PV = P \times \frac{1 - (1 + i)^{-n}}{i}
   \]
   where:
   - \(P = 250,000\) (quarterly payment),
   - \(i = 0.0125\) (quarterly interest rate),
   - \(n = 20\) (total number of payments).

3. **Total Economic Value**: Add the initial down payment to the present value of the quarterly payments.

### Calculations:

#### Present Value of Quarterly Payments:
\[
PV = 250,000 \times \frac{1 - (1 + 0.0125)^{-20}}{0.0125}
\]
\[
PV = 250,000 \times \frac{1 - (1.0125)^{-20}}{0.0125}
\]
\[
PV \approx 250,000 \times 16.56
\]
\[
PV \approx 4,140,000
\]

#### Total Economic Value:
\[
\text{Total Economic Value} = 1,000,000 + 4,140,000 = 5,140,000
\]

Thus, the economic value of the offer is approximately **₱5,140,000**. Based on the choices, the closest answer is **₱5,053,071.71**.

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Would you like further details or have any questions?

### Related Questions:
1. How is the quarterly compounding interest rate different from annual compounding?
2. Can the economic value change if payments were monthly instead of quarterly?
3. How does changing the interest rate affect the present value of the payments?
4. What if there was no down payment—how would that affect the economic value?
5. How do you calculate future values using compound interest?

#### Tip: Always adjust the interest rate according to the frequency of payments for accurate present value calculations.

Mr. Bitara received the following offer from Ms. Imatong on a housing lot that he wants to sell: ₱1,000,000 down plus ₱250,000 every end of the quarter for five years. Determine the economic value for the offer if the money can earn 5% compounded annually.

Calculate the economic value of Mr. Bitara's offer using present value of an annuity and compound interest formulas. The problem involves a ₱1,000,000 down payment and quarterly payments of ₱250,000 for five years at a 5% annual compounded rate.

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