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Part 1
Find the present value of the deposit.
​$28 comma 000 at 4.3​% compounded continuously for 7 years 
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Part 1
The present value is ​$
  
enter your response here. ​(Round to the appropriate​ cent.)

The formula for the present value (PV) of an amount compounded continuously is given by:

\[
PV = A \cdot e^{-rt}
\]

Where:
- $ A $ is the future value or final amount (in this case $28,000),
- $ r $ is the interest rate (4.3% or 0.043),
- $ t $ is the time in years (7 years),
- $ e $ is Euler's number (approximately 2.71828).

Now, we can plug in the values:

\[
PV = 28000 \cdot e^{-(0.043 \times 7)}
\]

Let me calculate the present value.The present value of the deposit is approximately \$20,722.18 when rounded to the nearest cent.

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. How does continuously compounded interest differ from simple interest?
2. What happens to the present value if the interest rate increases?
3. What is the future value if the initial deposit was \$20,722.18?
4. How does the length of time affect the present value in continuous compounding?
5. Can we use a different compounding method (e.g., monthly) for this problem?

**Tip:** When dealing with continuously compounded interest, the rate of compounding is constant, making it different from typical compounding intervals like monthly or annually.

Find the present value of the deposit. $28,000 at 4.3% compounded continuously for 7 years. Round to the appropriate cent.

Calculate the present value of a $28,000 deposit compounded continuously at a rate of 4.3% for 7 years. This problem explores continuous compound interest using the formula PV = A * e^(-rt) and applies exponential decay to find the present value. Suitable for high school or college-level students.

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