In 17 years, Selena Willow is to receive $300,000 under the terms of a trust established by her grandparents. Assuming an interest rate of 5.2%, compounded continuously, what is the present value of Selena's legacy? The present value of the legacy is $ (Round to the nearest cent as needed.)
In 17 years, Selena Willow is to receive $300,000 under the terms of a trust established by her grandparents. Assuming an interest rate of 5.2%, compounded continuously, what is the present value of Selena's legacy? The present value of the legacy is $ (Round to the nearest cent as needed.)
Chapter12: Sequences, Series And Binomial Theorem
Section12.3: Geometric Sequences And Series
Problem 12.59TI: New grandparents decide to invest 3200 per month in an annuity for their grandson, The account will...
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![### Present Value Calculation of Selena Willow's Trust Legacy
In 17 years, Selena Willow is to receive $300,000 under the terms of a trust established by her grandparents. Assuming an interest rate of 5.2%, compounded continuously, what is the present value of Selena's legacy?
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The present value of the legacy is $\[ \_\_\_\_\_\]
(Round to the nearest cent as needed.)
#### Explanation:
To find the present value (PV) of Selena's legacy, we use the formula for continuous compounding:
\[ PV = FV \cdot e^{-rt} \]
where:
- \( FV \) is the future value ($300,000),
- \( r \) is the interest rate (5.2% or 0.052),
- \( t \) is the time in years (17 years),
- \( e \) is the base of the natural logarithm (approximately 2.71828).
By substituting these values into the formula, we can determine the present value today that would grow to $300,000 in 17 years at an interest rate of 5.2%, compounded continuously. Once you have calculated the result, remember to round it to the nearest cent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F665b06fb-a73d-4402-a7e3-bb1a2d53162f%2F589b4709-c328-4479-8804-fcc922ce0414%2Fvb6fn59_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Present Value Calculation of Selena Willow's Trust Legacy
In 17 years, Selena Willow is to receive $300,000 under the terms of a trust established by her grandparents. Assuming an interest rate of 5.2%, compounded continuously, what is the present value of Selena's legacy?
---
The present value of the legacy is $\[ \_\_\_\_\_\]
(Round to the nearest cent as needed.)
#### Explanation:
To find the present value (PV) of Selena's legacy, we use the formula for continuous compounding:
\[ PV = FV \cdot e^{-rt} \]
where:
- \( FV \) is the future value ($300,000),
- \( r \) is the interest rate (5.2% or 0.052),
- \( t \) is the time in years (17 years),
- \( e \) is the base of the natural logarithm (approximately 2.71828).
By substituting these values into the formula, we can determine the present value today that would grow to $300,000 in 17 years at an interest rate of 5.2%, compounded continuously. Once you have calculated the result, remember to round it to the nearest cent.
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