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Phill and Laura Dutch have a new grandchild, Brenda. They want to create a trust fund for her that will yield $230,000 on her 25th birthday. a) What lump sum would they have to deposit now at 5.8%, compounded continuously, to achieve $230,000? b) Phill and Laura decide instead to invest a constant money stream of R(t) dollars per year. Find R(t) such that the accumulated future value of the continuous money stream is $230,000, assuming an interest rate of 5.8%, compounded continuously.

Phill and Laura Dutch have a new grandchild, Brenda. They want to create a trust fund for her that will yield $230,000 on her 25th birthday. a) What lump sum would they have to deposit now at 5.8%, compounded continuously, to achieve $230,000? b) Phill and Laura decide instead to invest a constant money stream of R(t) dollars per year. Find R(t) such that the accumulated future value of the continuous money stream is $230,000, assuming an interest rate of 5.8%, compounded continuously.

Intermediate Algebra
Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Exponential And Logarithmic Functions
Section11.2: Applications Of Exponential Functions
Problem 27PS
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Phill and Laura Dutch have a new grandchild, Brenda. They want to create a trust fund for her that will yield $230,000 on her 25th birthday. a) What lump sum would they have to deposit now at 5.8%, compounded continuously, to achieve $230,000? b) Phill and Laura decide instead to invest a constant money stream of R(t) dollars per year. Find R(t) such that the accumulated future value of the continuous money stream is $230,000, assuming an interest rate of 5.8%, compounded continuously. a) To achieve $230,000, they would have to deposit $ (Round to the nearest cent as needed.) b) To achieve $230,000, they would need a constant money stream of $ per year. (Round to the nearest cent as needed.)
Transcribed Image Text:Phill and Laura Dutch have a new grandchild, Brenda. They want to create a trust fund for her that will yield $230,000 on her 25th birthday. a) What lump sum would they have to deposit now at 5.8%, compounded continuously, to achieve $230,000? b) Phill and Laura decide instead to invest a constant money stream of R(t) dollars per year. Find R(t) such that the accumulated future value of the continuous money stream is $230,000, assuming an interest rate of 5.8%, compounded continuously. a) To achieve $230,000, they would have to deposit $ (Round to the nearest cent as needed.) b) To achieve $230,000, they would need a constant money stream of $ per year. (Round to the nearest cent as needed.)
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