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.