Find the present value PV of the given investment. (Round your answer to the nearest cent.)
An investment earns 2% per year and is worth $50,000 after 16 months.
PV = $   

To find the present value (PV) of an investment, we use the formula for the present value of an investment compounded annually:

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

where:
- $ FV $ is the future value of the investment,
- $ r $ is the annual interest rate (expressed as a decimal),
- $ t $ is the time in years.

### Given Data:
- Future Value ($ FV $): $50,000
- Annual Interest Rate ($ r $): 2% = 0.02
- Time ($ t $): 16 months = $\frac{16}{12} = \frac{4}{3} \approx 1.3333$ years.

### Calculation:
Substitute the values into the formula:

\[
PV = \frac{50000}{(1 + 0.02)^{1.3333}}
\]

\[
PV = \frac{50000}{(1.02)^{1.3333}}
\]

Calculating further:

\[
PV \approx \frac{50000}{1.02698} \approx 48694.12
\]

### Final Answer:
The present value (PV) of the investment is approximately **$48,694.12**.

Let me know if you want more details or have any questions! Here are some related questions:

1. How would the PV change if the interest rate was higher?
2. What is the future value if the present value is $48,694.12 and the time period is 16 months?
3. How does the time period affect the present value?
4. How do you calculate PV if the compounding is monthly instead of annually?
5. What happens to PV when the future value increases?

**Tip:** Understanding how changes in interest rate and time affect present value is crucial for investment analysis!

Find the present value PV of the given investment. (Round your answer to the nearest cent.) An investment earns 2% per year and is worth $50,000 after 16 months.

Learn how to calculate the present value (PV) of a $50,000 investment with a 2% annual interest rate over 16 months. This problem involves compound interest calculations, suitable for students in Grades 10-12, and covers key mathematical concepts like exponential functions and present value formulas.

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