This problem is a multi$-$step $($two parts$)$ problem.

Part A:

At t$=0,$ you purchase a $4-$year, $5$ percent coupon bond $($paid annually$)$ that is priced to yield $6$ percent continuously compounded $($YTM $=6\%$ continuously compounded$).$ The face value of the bond is $$1,000.$ The bond issuer is the U$.$S$.$ government $($no liquidity risk$).$

You are also given that your holding period $($investment horizon$)$ equals to $3\mathrm{.}70$ years$($t$=$T$=3\mathrm{.}70$ years$).($This number is close to the Duration of bond.$)$

Suppose that the market interest rate changes to $5\mathrm{.}50$ percent continuously compounded during the first year of your purchase $($within year $1),$ and it remains at that level for the remaining life of the bond.

Assume that, the reinvestment rate for the first coupon payment is the new interest rate, that is$,5\mathrm{.}50$ percent continuously compounded. In addition, you will reinvest the coupon payments in a zero$-$coupon bond.

What is the total amount $($total proceeds$)$ in US Dollars in your investment account at the end of your investment horizon $($t$=3\mathrm{.}70)$ years?

Total proceeds is the sum of amount from reinvestment of coupon payments and the bond's selling price.

$($Round$-$off to four decimal places, to obtain as accurate answer as possible on Canvas.$)$ This problem is a multi$-$step $($two parts$)$ problem.

Part A:

At $\backslash ($ t$=0\backslash ),$ you purchase a $4-$year, $5$ percent coupon bond $($paid annually$)$ that is priced to yield $6$ percent continuously compounded $($YTM $\backslash (=6\backslash \%\backslash )$ continuously compounded$).$ The face value of the bond is $\backslash (\backslash$$ $1,000\backslash ).$ The bond issuer is the U$.$S$.$ government $($no liquidity risk$).$

You are also given that your holding period $($investment horizon$)$ equals to $3\mathrm{.}70$ years $(\backslash (\backslash$mathrm$\{$t$\}=\backslash$mathrm$\{$T$\}=3\mathrm{.}70\backslash )$ years$).($This number is close to the Duration of bond.$)$

Suppose that the market interest rate changes to $5\mathrm{.}50$ percent continuously compounded during the first year of your purchase $($within year $1),$ and it remains at that level for the remaining life of the bond.

Assume that, the reinvestment rate for the first coupon payment is the new interest rate, that is$,5\mathrm{.}50$ percent continuously compounded. In addition, you will reinvest the coupon payments in a zero$-$coupon bond.

What is the total amount $($total proceeds$)$ in US Dollars in your investment account at the end of your investment horizon $\backslash (($t$=3\mathrm{.}70)\backslash )$ years?

Total proceeds is the sum of amount from reinvestment of coupon payments and the bond's selling price.

$($Round$-$off to four decimal places, to obtain as accurate answer as possible on Canvas.$)$