Annual payments of P12, 500 with interest rate of 10.5% compounded semi-annually for 6 years

To find the future value (FV) of a series of annual payments (also called an annuity) compounded semi-annually, we can use the future value of an annuity formula for compound interest. Given:

- Annual payment (\( R \)) = 12,500
- Interest rate (\( i \)) = 10.5% compounded semi-annually, so the semi-annual rate is 5.25% (or 0.0525 in decimal form).
- Number of years (\( t \)) = 6
- Since it's compounded semi-annually, the total number of compounding periods (\( n \)) = \( 6 \times 2 = 12 \)

We use the future value of an annuity formula for compounding at each payment period:
\[
FV = R \times \frac{(1 + i)^n - 1}{i}
\]

### Step 1: Plugging in the values
1. \( R = 12,500 \)
2. \( i = 0.0525 \)
3. \( n = 12 \)

\[
FV = 12,500 \times \frac{(1 + 0.0525)^{12} - 1}{0.0525}
\]

### Step 2: Calculate \((1 + i)^{n}\)
\[
(1 + 0.0525)^{12} = 1.0525^{12} \approx 1.8347
\]

### Step 3: Substitute into the formula
\[
FV = 12,500 \times \frac{1.8347 - 1}{0.0525}
\]
\[
FV = 12,500 \times \frac{0.8347}{0.0525}
\]

### Step 4: Final Calculation
\[
FV \approx 12,500 \times 15.8962 \approx 198,702.50
\]

### Conclusion
The future value of the annual payments after 6 years with semi-annual compounding at 10.5% interest is approximately **P198,702.50**.

Would you like more details, or do you have any questions?

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### Related Questions
1. How would the future value change if payments were made monthly?
2. What would the future value be if the interest rate were compounded quarterly instead of semi-annually?
3. How does the future value change if payments are made at the beginning of each period instead of the end?
4. What would be the future value if the compounding frequency matched the payment frequency?
5. What if the payment amount increased by a certain percentage each year?

### Tip
For annuities, align the compounding period with the payment frequency for accurate results!

Annual payments of P12,500 with interest rate of 10.5% compounded semi-annually for 6 years

This guide explains how to calculate the future value of an annuity with annual payments of P12,500 at a 10.5% interest rate, compounded semi-annually over 6 years. It includes step-by-step instructions, covering compound interest and annuity concepts. Ideal for college finance students.

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