To find the present value (PV) that will grow to $9000 in 10 years, with an annual interest rate of 4.5% compounded quarterly, we can use the compound interest formula:

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

Where:

• $A$ is the future value (which is $9000),
• $r$ is the annual interest rate (4.5% or 0.045),
• $n$ is the number of times the interest is compounded per year (quarterly means $n = 4$),
• $t$ is the number of years (which is 10 years).

Let's plug in the values and solve for $PV$:

$PV = \frac{9000}{(1 + \frac{0.045}{4})^{4 \times 10}}$

Now, let me calculate the present value.The present value that will grow to $9000 with a 4.5% annual interest rate compounded quarterly over 10 years is approximately $5753.09.

Would you like more details on the calculation, or do you have any other questions? Here are five related questions to explore further:

1. What is the future value if the present value is $5753.09, but the interest rate is different?
2. How does increasing the compounding frequency (e.g., monthly) affect the present value?
3. What would the present value be for a shorter time period, such as 5 years?
4. How does continuous compounding differ from quarterly compounding in this scenario?
5. How is the present value affected if the interest rate is compounded annually instead?

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