Consider the following bonds each of which is redeemable at par, pays semi$-$annual coupons, and has a yield rate of $5\%$ compounded semi$-$annually.

Suppose that a portfolio of bonds contains $9$ units of Bond A$,10$ units of Bond B$,$ and $9$ units of Bond C$.$

$($a$)$ Determine the present value of the portfolio of bonds.

Present Value of Portfolio $=$$

$($b$)$ Determine the duration $($to $3$ decimals$)$ of the portfolio of bonds.

Duration of Portfolio $=$

years

Note: Use all dollar values to the closest cent in your duration calculation.

$($c$)$ Use the duration to estimate the absolute and percentage $($or relative$)$ change in the portfolio value if the yield decreases by $0\mathrm{.}5\%.$

Estimated Absolute Change in Portfolio $=$$

Estimated Percent Change in Porftolio $=$

$\%($to $3$ decimals$)$

$[$Note: The changes should be positive if the portfolio value increases and negative if the portfolio value decreases.$]$