$($Solving for $r$ with annuities$)$ Nicki Johnson, a sophomore mechanical engineering student, receives a call from an insurance agent, who believes that Nicki is an older

woman ready to retire from teaching. He talks to her about several annuities that she could buy that would guarantee her an annual fixed income. The annuities are as

follows in the popup window: $.$

If Nicki could earn $9$ percent on her money by placing it in a savings account, should she place it instead in any of the annuities? Which ones, if any? Why?

a$.$ What rate of return could Nicki earn on her money if she place it in annuity A with $$7,500$ payment per year and $10$ years duration?

$\%($Round to two decimal places.$)$

If Nicki could earn $9$ percent on her money by placing it in a savings account, should she place it instead in annuity A$?($Select the best choice below.$)$

A$.$ Yes. Nicki should place her money in annuity A because the expected rate of return on the annuity is greater than the one on the savings account.

B$.$ No$.$ Nicki should not place her money in annuity A because the expected rate of return on the annuity is smaller than the one on the savings account.

b$.$ What rate of return could Nicki earn on her money if she place it in annuity annuity B with $$8,500$ payment per year and $15$ years duration?

$\%($Round to two decimal places.$)$

If Nicki could earn $9$ percent on her money by placing it in a savings account, should she place it instead in annuity B$?($Select the best choice below.$)$

A$.$ No$.$ Nicki should not place her money in annuity B because the expected rate of return on the annuity is smaller than the one on the savings account.

B$.$ Yes. Nicki should place her money in annuity B because the expected rate of return on the annuity is greater than the one on the savings account.

c$.$ What rate of return could Nicki earn on her money if she place it in annuity annuity $C$ with $$7,000$ payment per year and $12$ years duration?

$\%($Round to two decimal places.$)$

If Nicki could earn $9$ percent on her money by placing it in a savings account, should she place it instead in annuity $C?($Select the best choice below.$)$

A$.$ No$.$ Nicki should not place her money in annuity $C$ because the expected rate of return on the annuity is smaller than the one on the savings account.

B$.$ Yes. Nicki should place her money in annuity $C$ because the expected rate of return on the annuity is greater than the one on the savings account.