$2.$ After recently receiving a bonus, you have decided to add some bonds to your investment portfolio. You have narrowed your choice down to the following bonds $($assume semiannual payments$)$: Bond A Bond B Bond C Settlement Date $2/15/20152/15/20152/15/2015$ Maturity Date $8/15/20255/15/20356/15/2045$ Coupon Rate $5\mathrm{.}00\%7\mathrm{.}50\%8\mathrm{.}00\%$ Market Price $$987$ $$1,040$ $$1,098$ Face Value $$1,000$ $$1,000$ $$1,000$ Required Return $5\mathrm{.}25\%7\mathrm{.}00\%7\mathrm{.}25\%$ a$.$ Using the PRICE function, calculate the intrinsic value of each bond. Are any of the bonds currently undervalued? How much accrued interest would you have to pay for each bond? b$.$ Calculate the current yield of each bond. Is this the total return that you would earn each year? If you were on a fixed income, would you care about this number? c$.$ Using the YIELD function, calculate the yield to maturity of each bond using the current market prices. How do the YTMs compare to the current yields of the bonds? d$.$ Calculate the duration and modified duration of each bond. Create a chart that shows both measures versus term to maturity. Does duration increase linearly with term? If not, what relationship do you see? e$.$ Which bond would you rather own if you expect market rates to fall by $2\%$ for all bonds? What if rates will rise by $2\%?$ Why?