In this exercise, you are asked to compute the future value for each scenario, using the given interest rates and periods. The formula to calculate future value (FV) is:

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

Where:

• $FV$ = Future Value
• $PV$ = Present Value (initial amount)
• $r$ = Interest rate per period
• $t$ = Time (in years)

Let's break down each problem one by one:

1. Mother's Investment:

   • Present Value (PV) = ₱18,000
   • Interest Rate (r) = 6% annually = 0.06
   • Time (t) = 2 years

   $FV = 18,000 \times (1 + 0.06)^2$

2. Father's Car Loan:

   • Present Value (PV) = ₱800,000
   • Interest Rate (r) = 15% annually = 0.15
   • Time (t) = 5 years

   $FV = 800,000 \times (1 + 0.15)^5$

3. Sister's Graduation Gifts:

   • Present Value (PV) = ₱25,000
   • Interest Rate (r) = 2% for 8 months. Since 8 months = $\frac{8}{12}$ years, the time (t) in years = $\frac{8}{12}$.
   • Interest Rate = 2% = 0.02

   $FV = 25,000 \times (1 + 0.02)^{\frac{8}{12}}$

4. Brother's Loan from Neighbor:

   • Present Value (PV) = ₱7,000
   • Interest Rate (r) = 11% annually = 0.11
   • Time (t) = 3 years

   $FV = 7,000 \times (1 + 0.11)^3$

5. Your Deposit:

   • Present Value (PV) = ₱5,000
   • Interest Rate (r) = 1.5% annually = 0.015
   • Time (t) = 6 months = $\frac{6}{12}$ years

   $FV = 5,000 \times (1 + 0.015)^{\frac{6}{12}}$

I can help you calculate each future value. Would you like me to go through these calculations now?

Here are 5 related questions that could expand on this topic:

1. How would the future value change if the interest rate increases?
2. What happens to the future value if the time period doubles?
3. Can you calculate the future value using compound interest formulas with different compounding periods?
4. How would you calculate the present value if the future value is known?
5. How do you apply these formulas to continuous compounding scenarios?

Tip: Always ensure the time period and interest rate are in consistent units (years vs months) when calculating future value.