$3\mathrm{.}2(4)$ On May $15,2024,$ the price of the $6\mathrm{.}75$ s of May $15,2028,$ was $106-\frac{{21}^1}{8}.$ Use

a calculator or spreadsheet to find the yield of the bond.

$3\mathrm{.}7$ A newly retired lady of $60$ years of age is considering purchasing an annuity that

pays $$25,000$ every six months for the rest of her life. The cost of the annuity is

$$575,000.$ The lady expects a return rate of $6\%($for semiannually compounding$)$

from the annuity.

$3\mathrm{.}7\mathrm{.}1(4)$ If the lady expects to live $25$ years after retirement, will she purchase

the annuity?

$3\mathrm{.}7\mathrm{.}2(4)$ If the lady expects to live for $40$ years after retirement, will she purchase

the annuity?

$3\mathrm{.}8$ Suppose that your family has just purchased an apartment for $$8m$ with $20\%$

down payment and $80\%$ loan. Let the loan rate be $2\mathrm{.}5\%$ and the loan maturity be

$20$ years,

$3\mathrm{.}8\mathrm{.}1(4)$ find out the monthly payment.

$3\mathrm{.}8\mathrm{.}2(4)$ What will be the outstanding value of the loan five years later?