alculate the present value. (Round your answer to two decimal places.)
A = $45,000, r = 7% compounded monthly, t = 5 years

The present value $ P $ can be calculated using the formula for compound interest:

\[
P = \frac{A}{(1 + \frac{r}{n})^{nt}}
\]

where:
- $ A = 45,000 $: the future amount
- $ r = 0.07 $: annual interest rate (7%)
- $ n = 12 $: number of compounding periods per year (monthly compounding)
- $ t = 5 $: time in years

### Step-by-Step Calculation

1. Convert the rate to a decimal: $ r = 0.07 $.
2. Calculate the monthly compounding factor: $ \frac{r}{n} = \frac{0.07}{12} \approx 0.0058333 $.
3. Find the total number of compounding periods: $ nt = 12 \times 5 = 60 $.
4. Substitute these values into the formula:

   \[
   P = \frac{45,000}{(1 + 0.0058333)^{60}}
   \]

5. Calculate $ (1 + 0.0058333)^{60} \approx 1.4166 $.
6. Now divide the future value by this factor:

   \[
   P \approx \frac{45,000}{1.4166} \approx 31,758.05
   \]

### Answer
The present value is approximately **$31,758.05**.

Would you like further details on this calculation, or do you have any questions?

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Here are some related questions that might deepen your understanding:

1. How does changing the compounding frequency affect the present value?
2. What would the present value be if the interest rate were increased to 8%?
3. How would the calculation change if compounding were continuous?
4. What is the impact of extending the investment period to 10 years on the present value?
5. How do monthly and annual compounding compare in terms of their effect on the present value?

**Tip:** Compounding frequency significantly impacts the growth of investments; more frequent compounding leads to a higher future value and a lower present value for the same interest rate.

Calculate the present value. (Round your answer to two decimal places.) A = $45,000, r = 7% compounded monthly, t = 5 years

Learn how to calculate the present value of a $45,000 investment with a 7% annual interest rate compounded monthly over 5 years. This detailed solution includes the present value formula and the impact of monthly compounding, suitable for students in Grades 10-12.

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