A payment of ₱500 will be paid at the end of every year at 6% interest compounded annually for five years. Find its present value.

To find the present value of an annuity where payments are made at the end of each year, we use the Present Value of an Ordinary Annuity formula:

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

Where:
- \(PV\) = Present value of the annuity
- \(P\) = Payment per period = ₱500
- \(r\) = Interest rate per period = 6% = 0.06
- \(n\) = Number of periods = 5 years

### Step-by-Step Calculation:

1. **Identify the values:**
   \[
   P = 500, \quad r = 0.06, \quad n = 5
   \]

2. **Plug the values into the formula:**
   \[
   PV = 500 \times \left( \frac{1 - (1 + 0.06)^{-5}}{0.06} \right)
   \]

3. **Calculate \( (1 + r)^{-n} \):**
   \[
   (1 + 0.06)^{-5} = 1.338225
   \]

4. **Substitute this back into the formula:**
   \[
   PV = 500 \times \left( \frac{1 - \frac{1}{1.338225}}{0.06} \right)
   \]

5. **Simplify:**
   \[
   PV = 500 \times \left( \frac{1 - 0.747258}{0.06} \right)
   \]
   \[
   PV = 500 \times \left( \frac{0.252742}{0.06} \right)
   \]
   \[
   PV = 500 \times 4.21237
   \]

6. **Final result:**
   \[
   PV \approx 500 \times 4.21237 = 2106.185
   \]

Thus, the present value of the annuity is approximately **₱2,106.19**.

Would you like more details on any part of the calculation?

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Here are 5 related questions to expand your understanding:
1. How does the present value change if the interest rate increases to 8%?
2. What happens to the present value if payments are made semi-annually instead of annually?
3. Can you calculate the present value for different payment amounts over the same period?
4. How does the present value change if the number of periods increases to 10 years?
5. How does the present value formula differ if payments are made at the beginning of each period (annuity due)?

**Tip:** When solving annuity problems, carefully distinguish between ordinary annuities (payments at the end of each period) and annuities due (payments at the beginning). The formulas differ slightly!

Find the present value of an annuity with a ₱500 annual payment over 5 years at 6% interest compounded annually. This problem utilizes the present value formula for ordinary annuities, covering core concepts in finance mathematics and compound interest.

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