$(2$ pts$)$ What is the current price of a $$1,000$ face value, $6\%$ coupon bond that pays interest semiannually if the bond matures in ten years and has a yield$-$to$-$maturity of $5\mathrm{.}25\%($Compounded semi$-$annually$)$

$(2$ pts$)$ A bond has a YTM of $6\mathrm{.}5\%,$ a modified duration of $17\mathrm{.}43$ years, a duration of $18$ years and a $25$ year maturity. By what percentage will the bond's price change if market interest rates increase by $1\%?$

$(2$ pts$)$ A portfolio consists of three bonds as follows

$\backslash$table$[[,$Amount Invested,Bond Duration$],[$Bond A$,$$$1,000,6\mathrm{.}8$ years$],[$Bond B$,$$$4,000,2\mathrm{.}4$ years$],[$Bond C$,$$$5,000,14\mathrm{.}1$ years$]]$

What is the duration of the bond portfolio?

$(4$ pts$)$ Today $(4/15/24)$ you purchase a $$1000$ face value $7\%$ coupon bond paid semi$-$annually, with a YTM of $6\%($compounded semi$-$annually$)$ and $10$ years to maturity $($matures on $4/15/34).$

a$.$ What is the price you paid for the bond today?

b$.$ If interest rates remain constant and the YTM of the bond remains at $6\%(SA),$ what will be the price of bond in $1$ year on $(\frac{4}{15}\frac{?}{2025})?$

c$.$ If interest rates remain constant and the YTM of the bond remains at $6\%($SA$),$ what will be the price of bond in $2$ years $(\frac{4}{15}\frac{?}{2026})?$

d$.$ If interest raes change and the YTM of the bond decreases to $5\mathrm{.}2\%($SA$)$ in $2$ years, what will be the price of the bond in $2$ years $(\frac{4}{15}\frac{?}{2026})$ if the YTM decreases to $5\mathrm{.}2\%(SA)?$