For each of these situations, determine the savings amount. Use an online time value of money calculator, app, financial calculator, or spreadsheet software.

What would be the value of a savings account started with $850, earning 9 percent (compounded annually) after 14 years?

**Note: Round FV factor to 3 decimal places and final answer to the nearest whole dollar.**

Brenda Young desires to have $10,000 eight years from now for her daughter’s college fund. If she will earn 6 percent (compounded annually) on her money, what amount should she deposit now? Use the present value of a single amount calculation.

**Note: Round PV factor to 3 decimal places and final answer to the nearest whole dollar.**

What amount would you have if you deposited $3,000 a year for 25 years at 8 percent (compounded annually)?

**Note: Round discount factor to 3 decimal places and final answer to the nearest whole dollar.**

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.

For each of these situations, determine the savings amount. Use an online time value of money calculator, app, financial calculator, or spreadsheet software.

What would be the value of a savings account started with $850, earning 9 percent (compounded annually) after 14 years?

Brenda Young desires to have $10,000 eight years from now for her daughter’s college fund. If she will earn 6 percent (compounded annually) on her money, what amount should she deposit now? Use the present value of a single amount calculation.

What amount would you have if you deposited $3,000 a year for 25 years at 8 percent (compounded annually)?

Learn how to calculate the future value of savings, the present value for a college fund, and the future value of an annuity. This covers key concepts in financial mathematics, including time value of money, compound interest, and annuity calculations, with step-by-step solutions. Suitable for college-level students or those studying financial mathematics.

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