To find the total value (future value) of an investment compounded monthly, we use the formula:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $A$ is the future value of the investment.
• $P$ is the principal amount (₱12,000).
• $r$ is the annual interest rate (7% or 0.07).
• $n$ is the number of times the interest is compounded per year (monthly compounding, so $n = 12$).
• $t$ is the number of years the money is invested (10 years).

Let's calculate step by step:

1. Principal $P = ₱12,000$
2. Annual interest rate $r = 0.07$
3. Compounding frequency $n = 12$ (monthly)
4. Time $t = 10$ years

Plugging these values into the formula:

$A = 12,000 \left(1 + \frac{0.07}{12}\right)^{12 \times 10}$

First, simplify inside the parentheses:

$A = 12,000 \left(1 + 0.0058333\right)^{120}$ $A = 12,000 \left(1.0058333\right)^{120}$

Now, raise 1.0058333 to the power of 120:

$A = 12,000 \times 2.006096$

Finally, multiply by 12,000:

$A ≈ ₱24,073.15$

The total value of the investment after 10 years is approximately ₱24,073.15.

Would you like further details or have any questions? Here are some follow-up questions to explore the topic further:

1. How would the future value change with different interest rates?
2. What if the interest were compounded quarterly instead of monthly?
3. How does the formula change for simple interest instead of compound interest?
4. What is the effect of compounding more frequently on the future value?
5. How would inflation affect the real value of the future amount?

Tip: Compounding more frequently leads to higher future value because interest is applied on previously accumulated interest more often.