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Christine​ O'Brien, who is​ self-employed, wants to invest ​$80,000 in a pension plan. One investment offers...

Christine​ O'Brien, who is​ self-employed, wants to invest ​$80,000 in a pension plan. One investment offers 7​% compounded quarterly. Another offers 6.75​% compounded continuously. a. Which investment will earn the most interest in 4 ​years? b. How much more will the better plan​ earn? c. What is the effective rate in each​ case? d. If Ms.​ O'Brien chooses the plan with continuous​ compounding, how long will it take for her ​$80,000 to grow to ​$90, 000​? e. How long will it take for her ​$80,000 to grow to at least ​$90,000 if she chooses the plan with quarterly​ compounding? (Be​ careful; interest is added to the account only every​ quarter.)

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