Question 1190654
Here's how to calculate the present value of the ordinary annuity:

**1. Determine the effective interest rate per payment period:**

Since payments are semi-annual, but the interest is compounded annually we need to find the effective semi-annual rate.  We can't simply divide the annual rate by two, instead we find the equivalent rate such that if we compound the semi-annual rate twice we get the annual rate. The formula to convert is:

(1 + annual rate) = (1 + semi-annual rate)^2

(1 + 0.12) = (1 + semi-annual rate)^2

1.12 = (1 + semi-annual rate)^2

sqrt(1.12) = 1 + semi-annual rate

1.0583 = 1 + semi-annual rate

semi-annual rate = 1.0583 - 1

semi-annual rate = 0.0583 or 5.83%

**2. Determine the number of payment periods:**

* The annuity lasts for 12 years.
* Payments are made semi-annually, meaning twice a year.
* Number of payment periods (n) = 12 years * 2 payments/year = 24 periods

**3. Use the present value of an ordinary annuity formula:**

PV = PMT * [1 - (1 + r)^-n] / r

Where:

* PV = Present Value (what we want to find)
* PMT = Payment amount per period (8,000 pesos)
* r = Interest rate per period (0.0583 or 5.83% as a decimal)
* n = Number of periods (24)

**4. Calculate:**

PV = 8000 * [1 - (1 + 0.0583)^-24] / 0.0583

PV = 8000 * [1 - (1.0583)^-24] / 0.0583

PV = 8000 * [1 - 0.2452] / 0.0583

PV = 8000 * 0.7548 / 0.0583

PV = 8000 * 12.9468

PV ≈ 103,574.27 pesos

Therefore, the present value of the ordinary annuity is approximately 103,574.27 pesos.