An investment will pay you $89,000 in four years. Assume the appropriate discount rate is 8.25 percent compounded daily. What is the present value?

Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. Use 365 days in a year.

To find the present value (PV) of the investment, we use the formula for the present value of a lump sum with daily compounding interest:

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

Where:
- $ FV $ is the future value ($89,000),
- $ r $ is the annual discount rate (8.25% or 0.0825),
- $ n $ is the number of times the interest is compounded per year (365, since it's daily compounding),
- $ t $ is the time in years (4 years).

### Plugging in the values:
\[
PV = \dfrac{89,000}{(1 + \dfrac{0.0825}{365})^{365 \times 4}}
\]

Now, I'll calculate this step by step.The present value of the investment is approximately **$63,986.60**.

Would you like further clarification or details on any step of the calculation? 

Here are 5 related questions to deepen your understanding:
1. How does the frequency of compounding affect the present value of an investment?
2. What would the present value be if the interest were compounded annually instead of daily?
3. How would the present value change if the discount rate increased to 10%?
4. Can you calculate the future value if the present value is known and the interest rate is compounded daily?
5. How would you adjust the formula if the compounding period were quarterly?

**Tip:** The more frequently interest is compounded, the lower the present value will be, as interest accumulates faster.

An investment will pay you $89,000 in four years. Assume the appropriate discount rate is 8.25 percent compounded daily. What is the present value?

Learn how to calculate the present value of $89,000 in four years using a discount rate of 8.25% compounded daily. This detailed solution breaks down the compound interest formula step by step and demonstrates the impact of daily compounding on the present value. Ideal for finance students.

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