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# Answer the following.An investor has two bonds in her portfolio, Bond C and Bond Z. Each bond matures in 4 years, has a face value of 1,000 dollars, and has a yield to maturity of 8.2 percent. Bond C pays an 11.5 percent annual coupon, while Bond Z is a zero coupon bond.a. Assuming that the yield to maturity of each bond remains at 8.2 percent over the next 4 years, calculate the price of the bonds at each of the following years to maturity: Years to Maturity Price of Bond C Price of Bond Z 4 ________________ ________________ 3 ________________ ________________ 2 ________________ ________________ 1 ________________ ________________ 0 ________________ ________________ b. Plot the time path of prices for each bond.

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$a)$ First, we have to find out the price of bond $C$ by changing the year maturity by using the excel sheet which we denote with $P$, where the number of year maturity $(NPER)$ is $4,3,2,1,0$, Par value $(FV)$ is $\1,000$, Coupon annual $(PMT)$ is $\115$ and the Interest rate $(RATE)$ is $8.2\%$.

\begin{align*} P&=-PV(RATE,NPER,PMT,FV)\\[7pt] &=-PV(8.2\%,4 ,115,1000)\\[7pt] &= \1,108.82\\[12pt] P&=-PV(RATE,NPER,PMT,FV)\\[7pt] &=-PV(8.2\%, 3,115,1000)\\[7pt] &= \1,084.74\\[12pt] P&=-PV(RATE,NPER,PMT,FV)\\[7pt] &=-PV(8.2\%, 2,115,1000)\\[7pt] &= \1,058.69\\[12pt] P&=-PV(RATE,NPER,PMT,FV)\\[7pt] &=-PV(8.2\%, 1,115,1000)\\[7pt] &= \1,030.50\\[12pt] P&=-PV(RATE,NPER,PMT,FV)\\[7pt] &=-PV(8.2\%, 0,115,1000)\\[7pt] &= \1,000\\[12pt] \end{align*}

Therefore, the bond $C$ price at year maturity $4,3,2,1,0$ are $\boxed{\1108.82, \1084.74, \1,058.69, \1,030.50, \1000}$

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