Mr. Dela Cruz plans to invest money for 15 years. He pays P2 500 at the end of every month. The plan earns 3% interest rate compounded semiannually. How much will the money be after 15 years?

To determine the future value of Mr. Dela Cruz's investment, we can use the **Future Value of an Ordinary Annuity** formula, as he makes regular monthly payments at the end of each period:

\[
FV = P \times \frac{(1 + i)^n - 1}{i}
\]

where:
- \( P = 2500 \): the monthly payment,
- \( i \): the effective interest rate per period,
- \( n \): the total number of payments.

### Step 1: Determine the Effective Interest Rate per Period
Since the interest rate is compounded semiannually (twice a year), we need to find the equivalent monthly interest rate based on the semiannual rate.

1. **Annual nominal interest rate** = 3%
2. **Semiannual interest rate** \( = \frac{3\%}{2} = 1.5\% = 0.015\)
3. **Convert semiannual to monthly**:
   \[
   i = (1 + 0.015)^{\frac{1}{6}} - 1
   \]

### Step 2: Total Number of Payments
The investment is for 15 years, and he pays monthly, so:
\[
n = 15 \times 12 = 180 \text{ payments}
\]

### Step 3: Calculate the Future Value

Substituting values for \(P\), \(i\), and \(n\) into the formula will give the future value of the annuity. I’ll proceed with the calculations.The future value of Mr. Dela Cruz's investment after 15 years will be approximately **P566,589.28**.

Would you like a breakdown of these steps, or have any further questions?

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Here are five related questions you might find helpful:
1. How would the future value change if the interest rate were compounded monthly instead?
2. What if Mr. Dela Cruz increased his monthly payment by 10%?
3. How does the compounding frequency affect the overall future value of the investment?
4. What would the future value be if he invested for 20 years instead?
5. How would an interest rate change from 3% to 4% impact the final amount?

**Tip:** The more frequently an investment compounds, the greater the future value will be, due to interest on interest.

Mr. Dela Cruz plans to invest money for 15 years. He pays P2,500 at the end of every month. The plan earns a 3% interest rate compounded semiannually. How much will the money be after 15 years?

Learn to calculate the future value of Mr. Dela Cruz's investment, with monthly deposits of P2,500 over 15 years at a 3% interest rate compounded semiannually. This problem covers future value annuity calculations and compound interest for Grades 11-12.

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