$(1$ point$)($Exercise $3\mathrm{.}32)$ a$)$ Find the present value of an annuity$-$immediate which pays $1$ at the end of each half$-$year for $8$ years, if the

rate of interest is $6\mathrm{.}4\%$ convertible semiannually for the first $5$ years and $10\%$ convertible semiannually for the last $3$ years.

ANSWER $($round to $3$ decimal places$)=$

b$)$ Find the present value of an annuity$-$immediate which pays $1$ at the end of each half$-$year for $8$ years, if all payments in the first $5$

years are discounted at a nominal interest rate $6\mathrm{.}4\%$ convertible semiannually and all payments in the last $3$ years are discounted at a

nominal interest rate $10\%$ convertible semiannually.

ANSWER $($round off to three decimal digits$)=$