Christine O'Brien, who is self-employed, wants to invest

$50,000

in a pension plan. One investment offers

6%

compounded quarterly. Another offers

5.75%

compounded continuously.

a. Which investment will earn the most interest in

6

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

$50,000

to grow to

$70,000?

e. How long will it take for her

$50,000

to grow to at least

$70,000

if she chooses the plan with quarterly compounding? (Be careful; interest is added to the account only every quarter.)