Mr. Dela Cruz would like to save P300,000 for his son’s college education. How much should he deposit in a savings account every months for 10 years if interest is 1% compounded semi – annually?

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.

Mr. Dela Cruz would like to save P300,000 for his son’s college education. How much should he deposit in a savings account every month for 10 years if interest is 1% compounded semi-annually?

Discover how much Mr. Dela Cruz should deposit monthly to save P300,000 for his son’s college education over 10 years, given an interest rate of 1% compounded semi-annually. Learn key financial math concepts like the future value of an annuity and interest compounding.

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