Calculate the present value PV of an investment that will be worth $1,000 at the stated interest rate after the stated amount of time. HINT [See Quick Example 4.] (Round your answer to the nearest cent.)
9 years, at 2% per year, compounded annually
PV = $ 

To calculate the present value (PV) of an investment, you can use the formula for present value with compound interest:

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

Where:
- $PV$ is the present value (what we're solving for),
- $FV$ is the future value (in this case, \$1,000),
- $r$ is the annual interest rate (2%, or 0.02 as a decimal),
- $n$ is the number of years (9 years).

### Step-by-step solution:
1. The future value $FV = 1,000$.
2. The interest rate $r = 0.02$.
3. The number of years $n = 9$.

Now, plug these values into the formula:

\[
PV = \frac{1,000}{(1 + 0.02)^9}
\]

\[
PV = \frac{1,000}{(1.02)^9}
\]

\[
PV = \frac{1,000}{1.197992}
\]

\[
PV \approx 834.02
\]

### Final Answer:
The present value (PV) is approximately **\$834.02**.

Would you like further details or clarifications on this? 

Here are 5 related questions:
1. How does changing the interest rate affect the present value?
2. What happens to the present value if the time period is shorter?
3. How would continuous compounding change the formula?
4. What is the difference between simple and compound interest in PV calculations?
5. Can the present value be calculated for varying interest rates?

**Tip:** The higher the interest rate or the longer the time period, the lower the present value of a future amount.

Calculate the present value PV of an investment that will be worth $1,000 at the stated interest rate after the stated amount of time. HINT [See Quick Example 4.] (Round your answer to the nearest cent.) 9 years, at 2% per year, compounded annually. PV = $

Learn how to calculate the present value of an investment that will be worth $1,000 in 9 years with a 2% interest rate compounded annually. This example demonstrates the use of the compound interest formula and is suitable for high school students studying finance and exponential growth. The final result is approximately $834.02.

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