Question 1178719
Let's break down this problem to find the present worth of the annuity.

**Understanding the Annuity:**

* **Annuity Amount (PMT):** P250
* **Start Time:** End of the third year
* **End Time:** End of the fourth year
* **Annual Interest Rate (r):** 5% or 0.05

**Cash Flow Diagram:**

```
Time (Years):   0       1       2       3       4
Cash Flow:      0       0       0       250     250
```

**Calculations:**

1.  **Present Value at the End of Year 2:**

    * We need to calculate the present value of the annuity payments at the end of the second year (one year before the first payment).
    * This is a simple two-payment annuity.
    * Use the present value of an ordinary annuity formula:
        * PV = PMT * [(1 - (1 + r)^-n) / r]
        * PV = 250 * [(1 - (1.05)^-2) / 0.05]
        * PV = 250 * [(1 - 0.907029478) / 0.05]
        * PV = 250 * [0.092970522 / 0.05]
        * PV = 250 * 1.85941044
        * PV ≈ 464.85261
    * This means that at the end of year 2, the payments are worth about P464.85

2.  **Present Value at Time 0 (Now):**

    * Now, we need to discount the present value at the end of year 2 back to the present (time 0).
    * PV(at t=0) = PV(at t=2) / (1 + r)^2
    * PV(at t=0) = 464.85261 / (1.05)^2
    * PV(at t=0) = 464.85261 / 1.1025
    * PV(at t=0) ≈ 421.63502

**Therefore, the present worth of the P250 annuity is approximately P421.64.**