To find the present value $PV$ of a deposit compounded continuously, we use the formula:

$PV = \frac{A}{e^{rt}}$

Where:

• $A$ is the future value (in this case, $47,000),
• $r$ is the annual interest rate (7.6% or 0.076 as a decimal),
• $t$ is the time in years (8 years),
• $e$ is the base of the natural logarithm (approximately 2.71828).

Let's calculate it step by step:

1. $A = 47,000$
2. $r = 0.076$
3. $t = 8$

Now, compute $PV$:

$PV = \frac{47000}{e^{0.076 \times 8}}$

I'll calculate this.The present value of the deposit is approximately $25,588.62.

Would you like more details or have any further questions? Here are some related questions to explore:

1. What is the formula for continuously compounded interest?
2. How does the present value change with different interest rates?
3. How would the present value change if the interest was compounded annually instead of continuously?
4. What is the difference between simple interest and continuously compounded interest?
5. How can you calculate future value using continuous compounding?

Tip: For continuous compounding, the formula involves the exponential function $e^{rt}$, making it more effective for higher frequencies of interest calculations.