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The problem you uploaded involves calculating the future value for several financial scenarios using either Equation 5-2 or the FVIF (Future Value Interest Factor) table. Each scenario involves calculating future values given a principal amount, an interest rate, and a specific time period.

Here is the step-by-step approach to calculate each one using the future value formula:

### Future Value Formula (Equation 5-2):
\[
FV = PV \times (1 + r)^n
\]
Where:
- \(FV\) is the future value,
- \(PV\) is the present value (initial investment or loan),
- \(r\) is the interest rate per period (expressed as a decimal),
- \(n\) is the number of periods.

### 1. Your mother invested ₱18,000 at 6% for 2 years:
- **\(PV = 18,000\)**
- **\(r = 6\% = 0.06\)**
- **\(n = 2\) years**
\[
FV = 18,000 \times (1 + 0.06)^2 = 18,000 \times (1.06)^2 = 18,000 \times 1.1236 = 20,224.8
\]
So, the future value is **₱20,224.80**.

### 2. Your father obtained a loan of ₱800,000 at 15% for 5 years:
- **\(PV = 800,000\)**
- **\(r = 15\% = 0.15\)**
- **\(n = 5\) years**
\[
FV = 800,000 \times (1 + 0.15)^5 = 800,000 \times (1.15)^5 = 800,000 \times 2.011357 = 1,609,085.6
\]
So, the future value is **₱1,609,085.60**.

### 3. Your sister placed ₱25,000 in a special savings account at 2% for 8 months:
- **\(PV = 25,000\)**
- **\(r = 2\% = 0.02\)**
- **\(n = \frac{8}{12} = \frac{2}{3}\)** years (since 8 months is 2/3 of a year)
\[
FV = 25,000 \times (1 + 0.02)^{\frac{2}{3}} \approx 25,000 \times 1.0133 = 25,332.5
\]
So, the future value is **₱25,332.50**.

### 4. Your brother borrowed ₱7,000 at 11% for 3 years:
- **\(PV = 7,000\)**
- **\(r = 11\% = 0.11\)**
- **\(n = 3\) years**
\[
FV = 7,000 \times (1 + 0.11)^3 = 7,000 \times (1.11)^3 = 7,000 \times 1.367631 = 9,573.42
\]
So, the future value is **₱9,573.42**.

### 5. You deposited ₱5,000 at 1.5% for 6 months:
- **\(PV = 5,000\)**
- **\(r = 1.5\% = 0.015\)**
- **\(n = \frac{6}{12} = 0.5\)** years (since 6 months is half a year)
\[
FV = 5,000 \times (1 + 0.015)^{0.5} \approx 5,000 \times 1.00748 = 5,037.4
\]
So, the future value is **₱5,037.40**.

Let me know if you'd like further clarifications on any of these calculations or details about specific steps!

### Related Questions:
1. What effect does increasing the interest rate have on the future value over a fixed time period?
2. How would the future value change if your sister's savings duration was 12 months instead of 8 months?
3. If your brother's loan duration was 5 years instead of 3 years, what would the new future value be?
4. How would the future value calculation differ if the interest were compounded quarterly rather than annually?
5. What happens to the future value if the principal amount is doubled, but the interest rate and time remain the same?

### Tip:
Always express interest rates in decimal form and ensure the time period (years, months) matches the compounding interval to avoid errors in future value calculations.

Using the situations provided in Exercise 1, compute for the future value at the end of the term for each scenario using Equation 5-2 or the FVIF table.

Learn how to compute future values for various financial situations using the Future Value Formula (FV = PV * (1 + r)^n). This problem includes calculating future values for investments and loans, with specific interest rates and time periods.

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