To solve the problem, we use the formula for compound interest:

$A = P(1 + r)^n$

Where:

• $A$ = Maturity value
• $P$ = Principal amount ($\text{Php} 30,000$)
• $r$ = Annual interest rate in decimal ($4.5\% = 0.045$)
• $n$ = Number of compounding periods ($3$ years)

Step 1: Calculate the maturity value

Substitute the given values into the formula:

$A = 30,000 \times (1 + 0.045)^3$

First, calculate $(1 + 0.045)$:

$1 + 0.045 = 1.045$

Now raise $1.045$ to the power of 3:

$1.045^3 = 1.141166$

Multiply by the principal:

$A = 30,000 \times 1.141166 = 34,235.00$

Step 2: Calculate the compound interest

The compound interest is the difference between the maturity value and the principal:

$\text{Compound Interest} = A - P = 34,235.00 - 30,000 = 4,235.00$

Final Answer:

• Maturity Value: Php 34,235.00
• Compound Interest: Php 4,235.00

Would you like further details or an explanation of any step? Here are some related questions:

1. What is the difference between simple and compound interest?
2. How does changing the interest rate affect the maturity value?
3. What happens if the compounding frequency is increased to semi-annually or quarterly?
4. Can we derive the formula for compound interest from basic principles?
5. How would inflation impact the real value of the maturity amount?

Tip: Always double-check calculations involving exponents to ensure precision, especially when dealing with financial data.