To solve the problems in Exercise 4, we will use the Future Value (FV) formula:

$FV = PV \times (1 + r)^t$

Where:

• PV = Present Value (initial investment or loan)
• r = annual interest rate (in decimal form, i.e., 6% = 0.06)
• t = time in years

Let’s solve each scenario:

1. Your mother invested ₱18,000 at 6% annually for two years:

$FV = 18,000 \times (1 + 0.06)^2 = 18,000 \times (1.06)^2 = 18,000 \times 1.1236 = 20,224.80$

So, the future value is ₱20,224.80.

2. Your father obtained a car loan for ₱800,000 at 15% annual rate for five years:

$FV = 800,000 \times (1 + 0.15)^5 = 800,000 \times (1.15)^5 = 800,000 \times 2.0114 = 1,609,120$

The future value of the loan is ₱1,609,120.

3. Your sister placed ₱25,000 in a savings account that provides 2% interest for 8 months:

Since 8 months is $\frac{8}{12} = \frac{2}{3}$ years, we compute:

$FV = 25,000 \times (1 + 0.02)^{\frac{2}{3}} = 25,000 \times (1.0133) = 25,333.33$

The future value is ₱25,333.33.

4. Your brother borrowed ₱7,000 from a neighbor at 11% for 3 years:

$FV = 7,000 \times (1 + 0.11)^3 = 7,000 \times (1.11)^3 = 7,000 \times 1.3676 = 9,573.20$

The future value is ₱9,573.20.

5. You deposited ₱5,000 in a time deposit account with 1.5% for 6 months:

6 months is $\frac{6}{12} = 0.5$ years:

$FV = 5,000 \times (1 + 0.015)^{0.5} = 5,000 \times 1.0075 = 5,037.50$

The future value is ₱5,037.50.

Would you like further details on any step? Let me know if you have questions!

Here are some follow-up questions:

1. How does compounding frequency affect the future value in these calculations?
2. What would be the difference in future value if interest was compounded monthly instead of annually?
3. Can we solve similar problems using a financial calculator?
4. How would the results change if we changed the interest rate by 1% in each scenario?
5. What is the formula to compute future value with continuous compounding?

Tip: For short-term investments or loans (less than a year), ensure to adjust the time period accurately based on months or fractions of a year.