What is the present value of an annuity ₱875 payable monthly for 5 years and 6 months with an interest rate at 6% compounded semi annually 

To find the present value of an annuity, we use the following formula:

\[
PV = P \times \left[ \frac{1 - (1 + r)^{-n}}{r} \right]
\]

Where:
- \(PV\) is the present value of the annuity.
- \(P\) is the payment amount per period.
- \(r\) is the periodic interest rate.
- \(n\) is the total number of payments.

Given:
- Monthly payment \(P = ₱875\)
- Number of years \(t = 5.5\) years (which is 5 years and 6 months)
- Interest rate per year \(i = 6\%\), compounded semi-annually.

First, we need to find the effective monthly interest rate:

### Step 1: Convert the annual interest rate to the monthly interest rate.
- Since the interest is compounded semi-annually, the semi-annual interest rate is:
  \[
  \text{Semi-annual rate} = \frac{6\%}{2} = 3\% = 0.03
  \]
- The effective monthly rate \(r\) is calculated by converting the semi-annual rate:
  \[
  r = \left(1 + 0.03\right)^{\frac{1}{6}} - 1
  \]

### Step 2: Calculate the total number of payments.
- Total number of payments \(n\) is:
  \[
  n = 5.5 \text{ years} \times 12 \text{ months/year} = 66 \text{ months}
  \]

### Step 3: Substitute the values into the present value formula.

Let me calculate this for you.The present value of the annuity is approximately **₱49,179.99**.

Would you like more details or have any questions about the calculation? Here are five related questions that might interest you:

1. How does the compounding frequency affect the present value of an annuity?
2. What if the interest rate were compounded monthly instead of semi-annually?
3. How would the present value change if the payment period were different?
4. Can this formula be used for annuities with varying payments?
5. How does the present value differ between ordinary annuities and annuities due?

**Tip:** Always check the compounding period when dealing with interest rates, as it significantly affects the calculations.

Learn how to calculate the present value of an annuity paying ₱875 monthly for 5 years and 6 months at a 6% interest rate compounded semi-annually. This problem involves financial calculations using the Present Value of Annuity formula. Suitable for advanced learners and professionals in finance.

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