Calculate the present value *PV* (in dollars) of an investment that will be worth $1,000 at the stated interest rate after the stated amount of time. (Round your answer to the nearest cent.)

9years, at5.4% per year, compounded quarterly

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

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

Where:
- $ FV $ is the future value (in this case, $1,000),
- $ r $ is the annual interest rate (expressed as a decimal),
- $ n $ is the number of compounding periods per year,
- $ t $ is the number of years.

Given:
- $ FV = 1000 $,
- $ r = 5.4\% = 0.054 $,
- $ n = 4 $ (since the interest is compounded quarterly),
- $ t = 9 $ years.

Now, let's substitute these values into the formula and calculate the present value.

\[
PV = \frac{1000}{\left(1 + \frac{0.054}{4}\right)^{4 \times 9}}
\]

I'll calculate that now.The present value (PV) of the investment is **$617.08**.

Would you like any further clarification or details on this calculation?

Here are some related questions:
1. How does changing the compounding frequency affect the present value?
2. What would the present value be if the interest rate was 6% instead of 5.4%?
3. How does the investment period affect the present value?
4. What is the difference between simple and compound interest in such calculations?
5. How would continuous compounding change the present value?

**Tip:** The more frequently interest is compounded, the higher the future value grows for the same interest rate and time period.

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. 9 years, at 5.4% per year, compounded quarterly.

Learn how to calculate the present value (PV) of an investment worth $1,000 in 9 years with a 5.4% annual interest rate, compounded quarterly. The detailed solution uses the compound interest formula and explains key concepts for Grades 10-12 students.

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