The present value of FV dollars compounded at an interest rate i per period for n periods is PV=FV/(1+i)^n. In the formula, PV represents the present value, FV is the future value after n compounding periods. When the annual interest i is compounded m times per year, the interest rate per period is understood to be i/m. Find the present value of the given future amount of $10,752.34 at 3.3% compounded annually for 5 years.​(Do not round until the final answer. Then round to the nearest cent as​ needed.) 

To solve this problem, we will use the present value formula:

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

where:
- $ FV = 10,752.34 $ (the future value),
- $ i = 0.033 $ (3.3% annual interest rate),
- $ n = 5 $ years (since it's compounded annually, $ n $ is 5).

Now, let's plug in the values into the formula:

\[
PV = \frac{10,752.34}{(1 + 0.033)^5}
\]

Step-by-step calculation:

1. Calculate $ 1 + 0.033 = 1.033 $.
2. Raise 1.033 to the power of 5:

\[
1.033^5 = 1.175276
\]

3. Divide the future value by this result:

\[
PV = \frac{10,752.34}{1.175276} \approx 9149.41
\]

So, the present value is approximately **$9,149.41**.

Would you like further details or have any questions?

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Here are 5 related questions you might find helpful:
1. How does the compounding frequency affect the present value calculation?
2. What would be the present value if the interest rate increased to 5%?
3. How do we calculate present value for continuous compounding?
4. What happens to the present value if the future value increases?
5. How does the time period (n) impact the present value?

**Tip:** The more frequent the compounding, the lower the present value will be for the same future amount.

The present value of FV dollars compounded at an interest rate i per period for n periods is PV=FV/(1+i)^n. In the formula, PV represents the present value, FV is the future value after n compounding periods. When the annual interest i is compounded m times per year, the interest rate per period is understood to be i/m. Find the present value of the given future amount of $10,752.34 at 3.3% compounded annually for 5 years.​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

Learn how to calculate the present value of a future amount of $10,752.34 with a 3.3% interest rate compounded annually for 5 years. This problem explores key financial mathematics concepts like compound interest and exponential growth, providing a detailed solution for students in Grades 11-12.

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