A $$100,000,168-$day Government of Canada Treasury bill was purchased on its date of issue to yield $3\mathrm{.}5\%.$

a$.$ What price did the investor pay? $($Do not round the intermediate calculations. Round your answer to $2$ decimal places.$)$

Price $

b$.$ Calculate the market value of the T$-$bill $85$ days later if the annual rate of return then required by the market has $($Do not round the intermediate calculations. Round your answers to $2$ decimal places.$)$:

$($i$)$ risen to $4\mathrm{.}1\%.$ $

$($ii$)$ remained at $3\mathrm{.}5\%.$ $

$($iii$)$ fallen to $2\mathrm{.}9\%.$ $

c$.$ What rate of return was realized by the investor $85$ days later if the T$-$bill was sold at a market rate of: $4\mathrm{.}1\%,3\mathrm{.}5\%,2\mathrm{.}9\%($Do not round the intermediate calculations. Round your answers to $3$ decimal places$)$:

$($i$)$ risen to $4\mathrm{.}1\%.$

$\%$

$($ii$)$ remained at $3\mathrm{.}5\%.$

$\%$

$($iii$)$ fallen to $2\mathrm{.}9\%.$

$\%$