Christine O'Brien, who is self-employed, wants to invest $40,000 in a pension plan. One investment a. Choose the investment which will earn the most interest below offers 8% compounded quarterly. Another offers 7.75% compounded continuously a. Which investment will earn the most interest in 5 years? b. How much more will the better plan earn? O compounded quarterly c. What is the effective rate in each case? O compounded continuously d. If Ms. O'Brien chooses the plan with continuous compounding, how long will it take for her $40,000 to grow to $90,000? b. The difference is $ e. How long will it take for her $40,000 to grow to at least $90,000 if she chooses the plan with quarterly (Round to the nearest cent as needed.) compounding? (Be careful, interest is added to the account only every quarter.) c. The effective rate for investment compounded quarterly is% (Round to the nearest hundredth as needed.) The effective rate for investment compounded continuously is% (Round to the nearest hundredth as needed.) d. years is needed to grow $40,000 to $90,000 with continuous compound interest. (Type an integer or a decimal rounded to the nearest hundredth.) e. years is needed to grow $40,000 to at least $90,000 with quarterly compound interest. (Type an integer or a decimal rounded to the nearest hundredth.)