Find the present value of $30,000 due in 2 years at the given rate of interest. (Use a 365-day year. Round your answer to the nearest cent.)

3%/year compounded monthly

To find the present value $ PV $ of a future amount due in $ t $ years at an interest rate $ r $ compounded monthly, you can use the formula:

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

Where:
- $ A $ is the future amount ($30,000),
- $ r $ is the annual interest rate (3% or 0.03),
- $ n $ is the number of compounding periods per year (12 for monthly compounding),
- $ t $ is the time in years (2 years).

Substituting the values:

\[
PV = \frac{30,000}{\left(1 + \frac{0.03}{12}\right)^{12 \times 2}}
\]

Let's calculate the present value.The present value $ PV $ of $30,000 due in 2 years at an interest rate of 3% per year, compounded monthly, is **$28,255.05**.

Would you like any further details or have any questions?

Here are some related questions you might find helpful:

1. How would the present value change if the interest were compounded quarterly instead of monthly?
2. What is the formula for present value when interest is compounded continuously?
3. How does the present value change with different interest rates?
4. What is the present value of $50,000 due in 5 years at 4% compounded monthly?
5. How does the time period affect the present value for a given interest rate?

**Tip:** Present value decreases as the compounding frequency increases, meaning you need to invest less today to reach a future amount when interest is compounded more frequently.

Learn how to calculate the present value of $30,000 due in 2 years at an annual interest rate of 3%, compounded monthly. Use our detailed step-by-step solution to understand compound interest calculations effectively.

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