Find the present value of $50,000 due in 4 years at the given rate of interest. (Use a 365-day year. Round your answer to the nearest cent.)

5%/year compounded daily

$

To find the present value of $50,000 due in 4 years at an interest rate of 5% compounded daily, we use the following formula for compound interest:

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

Where:
- $ PV $ is the present value (what we are solving for),
- $ FV = 50,000 $ is the future value,
- $ r = 0.05 $ (5% annual interest rate),
- $ n = 365 $ (compounded daily),
- $ t = 4 $ years.

Now, plugging in the values:

\[
PV = \frac{50,000}{(1 + \frac{0.05}{365})^{365 \times 4}}
\]

Let's compute this step by step.

1. Calculate $ \frac{0.05}{365} $:
   \[
   \frac{0.05}{365} = 0.000136986
   \]

2. Add 1 to the result:
   \[
   1 + 0.000136986 = 1.000136986
   \]

3. Raise this result to the power of $ 365 \times 4 = 1460 $:
   \[
   (1.000136986)^{1460}
   \]

4. Finally, divide the future value by this result to find the present value $ PV $.

Let me compute that for you.The present value of $50,000 due in 4 years at an interest rate of 5% compounded daily is approximately **$40,937.10**.

Would you like more details or have any other questions?

Here are 5 related questions to expand on this concept:
1. How would the present value change if the interest rate were 6% instead of 5%?
2. What would be the future value of $50,000 after 4 years at the same 5% interest rate compounded daily?
3. How does compounding frequency affect the present value compared to simple interest?
4. How would the present value calculation change if the compounding were monthly instead of daily?
5. What is the formula for present value if the interest is compounded continuously?

**Tip**: The more frequent the compounding, the smaller the present value, as the interest accrues more frequently.

Find the present value of $50,000 due in 4 years at the given rate of interest. (Use a 365-day year. Round your answer to the nearest cent.) 5%/year compounded daily

Learn how to calculate the present value of $50,000 due in 4 years with a 5% annual interest rate compounded daily. This example covers key concepts of compound interest and provides a step-by-step solution. Suitable for high school students in Grades 10-12.

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