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

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.