A MAT135 student wants to start investing their money for retirement. Microsoft currently has stock price of $295.90 per share, and a historic growth rate corresponding to an annual interest rate of 189 compounded continuously (measured from 2008). The student buys 10 Microsoft stocks. The investment follov this model: P(t) = Poe"t where P(t) is the price of the investment at time t (in years), r is the interest rate, and Po is the initial price c the investment. (a) If you need $1 million to retire, in how many years can this MAT135 student retire? Show your work and round your final answer to 2 decimal places. (b) The student will have to pay tax on the investment. To earn $1 million, the value of the investment must be $2 million. Considering taxes, how much longer will it take before the student can retire, compared to your answer in part (a)? Answer in years, and round to 2 decimal places.
A MAT135 student wants to start investing their money for retirement. Microsoft currently has stock price of $295.90 per share, and a historic growth rate corresponding to an annual interest rate of 189 compounded continuously (measured from 2008). The student buys 10 Microsoft stocks. The investment follov this model: P(t) = Poe"t where P(t) is the price of the investment at time t (in years), r is the interest rate, and Po is the initial price c the investment. (a) If you need $1 million to retire, in how many years can this MAT135 student retire? Show your work and round your final answer to 2 decimal places. (b) The student will have to pay tax on the investment. To earn $1 million, the value of the investment must be $2 million. Considering taxes, how much longer will it take before the student can retire, compared to your answer in part (a)? Answer in years, and round to 2 decimal places.
Chapter6: Exponential And Logarithmic Functions
Section6.7: Exponential And Logarithmic Models
Problem 16TI: Recent data suggests that, as of 2013, the rate of growth predicted by Moore’s Law no longer holds....
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Transcribed Image Text:A MAT135 student wants to start investing their money for retirement. Microsoft currently has a
stock price of $295.90 per share, and a historic growth rate corresponding to an annual interest rate of 18%,
compounded continuously (measured from 2008). The student buys 10 Microsoft stocks. The investment follows
this model:
P(t) = Poe"t
where P(t) is the price of the investment at time t (in years), r is the interest rate, and Po is the initial price of
the investment.
(a) If you need $1 million to retire, in how many years can this MAT135 student retire? Show your work and
round your final answer to 2 decimal places.
(b) The student will have to pay tax on the investment. To earn $1 million, the value of the investment must
be $2 million. Considering taxes, how much longer will it take before the student can retire, compared
to your answer in part (a)? Answer in years, and round to 2 decimal places.
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