To calculate the total amount of a series of monthly payments with interest compounded monthly, we use the formula for the Future Value of an Ordinary Annuity:

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

where:

• $P$ is the monthly payment amount,
• $r$ is the monthly interest rate,
• $n$ is the total number of payments.

Step 1: Identify the variables

Given:

• Monthly payment ($P$) = 3,000
• Number of years = 4
• Interest rate (annual) = 3%

Step 2: Convert the annual interest rate to a monthly rate

The monthly interest rate ($r$) is: $r = \frac{3\%}{12} = 0.03 / 12 = 0.0025$

Step 3: Calculate the total number of payments

Since payments are made monthly for 4 years: $n = 4 \times 12 = 48$

Step 4: Plug in values and calculate $FV$

$FV = 3,000 \times \frac{(1 + 0.0025)^{48} - 1}{0.0025}$

Let me calculate that for you.The future value of the monthly payments is approximately PHP 152,793.63 after 4 years at a 3% interest rate compounded monthly.

Would you like a more detailed breakdown or have any questions?

Here are some related questions you might explore:

1. How would changing the interest rate to 5% affect the total future value?
2. What if payments were made quarterly instead of monthly?
3. How is the formula different if interest is compounded annually?
4. What would be the present value of these payments instead of the future value?
5. How much total interest is earned over the 4 years?

Tip: For annuity problems, always confirm if payments are made at the beginning or end of each period; this determines if it’s an "ordinary annuity" or an "annuity due."