Let's go through each situation one by one, using the relevant time value of money formulas.

---

1. Future Value of a Single Amount (Compounded Annually)

You start with $850 in a savings account earning 9% compounded annually for 14 years.

The formula for the Future Value (FV) is:

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

Where:

• $PV = 850$ (the initial deposit)
• $r = 0.09$ (the annual interest rate)
• $n = 14$ (the number of years)

Now, calculate the Future Value factor:

$(1 + 0.09)^{14} = 1.09^{14} \approx 3.321$

Now, compute the future value:

$FV = 850 \times 3.321 = 2822.85$

Rounding to the nearest whole dollar:

$\boxed{FV = 2,823}$

---

2. Present Value for College Fund (Compounded Annually)

Brenda wants to have $10,000 in 8 years, earning 6% annually. We need to find the Present Value (PV), which is the amount she should deposit now.

The formula for Present Value (PV) is:

$PV = \frac{FV}{(1 + r)^n}$

Where:

• $FV = 10,000$ (the future value she wants)
• $r = 0.06$ (the annual interest rate)
• $n = 8$ (the number of years)

Now, calculate the Present Value factor:

$(1 + 0.06)^{8} = 1.06^8 \approx 1.593$

Now, compute the present value:

$PV = \frac{10,000}{1.593} \approx 6,278.59$

Rounding to the nearest whole dollar:

$\boxed{PV = 6,279}$

---

3. Future Value of an Annuity (Compounded Annually)

You deposit $3,000 every year for 25 years at 8% interest compounded annually. We need to find the Future Value of an Annuity (FVA).

The formula for Future Value of an Annuity is:

$FVA = P \times \frac{(1 + r)^n - 1}{r}$

Where:

• $P = 3,000$ (annual payment)
• $r = 0.08$ (annual interest rate)
• $n = 25$ (the number of years)

Now, calculate the Future Value of Annuity factor:

$\frac{(1 + 0.08)^{25} - 1}{0.08} = \frac{1.08^{25} - 1}{0.08} \approx \frac{6.848 - 1}{0.08} = 73.103$

Now, compute the future value of the annuity:

$FVA = 3,000 \times 73.103 \approx 219,309$

Rounding to the nearest whole dollar:

$\boxed{FVA = 219,309}$

---

Recap of Calculations:

1. Future Value of $850 after 14 years at 9%: $2,823
2. Present Value to have $10,000 after 8 years at 6%: $6,279
3. Future Value of Annuity of $3,000 for 25 years at 8%: $219,309

---

Would you like further details on any of these calculations or explanations?

Here are 5 related questions to explore further:

1. How does compounding frequency affect the future value of savings?
2. What is the difference between simple interest and compound interest?
3. How can you calculate the present value of an annuity?
4. What factors influence how much money you need to save for retirement?
5. What are some strategies to increase savings for long-term goals?

Tip: Always double-check interest rate compounding frequency (annually, semi-annually, etc.) as it can significantly affect calculations.