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Let's break down the problem step by step.

### Problem Details:
1. **Principal (P)**: ₱1,000.00
2. **Interest rate (r)**: 5% annually = 0.05
3. **Compounding period**: Annually
4. **Time (t)**: Variable (for part a) and 2 years (for part b)

### a. The equation for compound interest:
The formula for compound interest is:

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

Where:
- \(A\) is the amount of money after \(t\) years,
- \(P\) is the principal amount,
- \(r\) is the annual interest rate (in decimal form),
- \(n\) is the number of times the interest is compounded per year (for annual compounding, \(n = 1\)),
- \(t\) is the time in years.

For this case, since the interest is compounded annually (\(n = 1\)):

\[
A = 1000 \left(1 + 0.05\right)^{t}
\]

\[
A = 1000 \times (1.05)^t
\]

### b. Amount after 2 years:
To find the amount after 2 years, substitute \(t = 2\) into the equation:

\[
A = 1000 \times (1.05)^2
\]

First, calculate:

\[
A = 1000 \times 1.1025 = 1102.50
\]

So, the amount after 2 years will be **₱1,102.50**.

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

Here are 5 related questions:
1. How does the frequency of compounding affect the final amount?
2. What would the amount be after 5 years with the same conditions?
3. How would the formula change if interest were compounded monthly?
4. How does compound interest differ from simple interest in this scenario?
5. What is the total interest earned after 2 years?

**Tip:** Remember that compound interest grows exponentially, so the longer you leave the money invested, the more you benefit from it!

Alex deposited ₱1,000.00 in a bank at Puerto Galera that pays 5% compound interest annually. a. What equation best describes this investment after years? b. How much money will he have after 2 years?

Learn how to calculate the compound interest on a ₱1,000 deposit with a 5% annual interest rate. Find the equation that describes the investment over time and calculate the amount after 2 years.

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