Aziz works for a broker. One of his clients is offered a bond at $$1,050.$ It is a $10\%,15-$year bond with a par value of $$1,000$ and a call price of $$1,100.($The bond$$s first call date is in five years.$)$ Coupon payments are made semiannually.

a$.$ Find the current yield, YTM$,$ and YTC on this issue. Which of these three yields is the highest? Which is the lowest?

b$.$ Assume that the price of the bond declines to $$875.$ Now which yield is the highest? Which is the lowest?

An investor wants to find the duration of a $25-$year, $6\%$ semiannual$-$pay, noncallable bond that$$s currently priced in the market at $$882\mathrm{.}72$ to yield $7\%.$ Using a $50$ basis point change in yield, find the effective duration of this bond. $($Hint: Use Equation $11\mathrm{.}11.$ from Ch$.11)$