To solve the problem, we need to find out how much Mr. Dela Cruz should deposit monthly to save ₱300,000 in 10 years. The interest rate is 1% compounded semi-annually.

This is a future value of an ordinary annuity problem. Here's the breakdown:

Given:

• Future Value (FV) = ₱300,000
• Number of years = 10 years
• Interest rate = 1% compounded semi-annually
• Number of deposits per year = 12 (since monthly deposits)

Step 1: Convert interest rate and compounding

Since the interest is compounded semi-annually, we need to adjust it for monthly deposits.

• Semi-annual interest rate = 1% / 2 = 0.5% or 0.005 as a decimal.
• Since there are 12 months in a year, we’ll use this rate to calculate the monthly rate.

However, the compounding periods are semi-annual (twice a year), not monthly, so we should use the future value formula for an ordinary annuity, accounting for semi-annual compounding.

Step 2: Formula for future value of an annuity with semi-annual compounding

The formula is:

$FV = P \times \frac{(1 + r/n)^{nt} - 1}{r/n}$

Where:

• $FV$ is the future value (₱300,000),
• $P$ is the monthly payment (what we are solving for),
• $r$ is the annual interest rate (1% or 0.01),
• $n$ is the number of compounding periods per year (2, since it's semi-annual),
• $t$ is the number of years (10 years).

Step 3: Solving the equation

We can now solve this equation for $P$, the monthly payment, by rearranging the formula:

P = \frac{FV \times \frac{r/n}{(1 + r/n)^{nt} - 1}}

Let me calculate it for you:Mr. Dela Cruz should deposit approximately ₱14,299.94 every month for 10 years in order to save ₱300,000, given an interest rate of 1% compounded semi-annually.

Would you like to go over the steps in more detail or have any further questions?

Here are 5 related questions you might find helpful:

1. How does compounding frequency affect the total amount saved?
2. What if the interest rate were compounded monthly instead of semi-annually?
3. How would the monthly deposit change if the interest rate increased to 2%?
4. What if Mr. Dela Cruz wanted to save for 15 years instead of 10?
5. How does this calculation change if withdrawals are allowed during the savings period?

Tip: The higher the compounding frequency, the more interest you accumulate over time, which can lower the required monthly payments.