$(1)$ The Zeniba Corp. has bonds outstanding that mature $10$ years from today. The bonds

have a fixed coupon $=6\mathrm{.}30\%,$ pay interest semiannually, and have a face value $=$$$1,000\mathrm{.}00.$

Today investors require an average annual rate of return on $10$ year loans to Zeniba $($i$.$e$.,$ a

yield to maturity$)=7\mathrm{.}5\%$

a$)$ What do you estimate, to the nearest penny, is today's price per bond?

b$)$ Suppose the annual return required by investors on $10$ year loans to Zeniba suddenly rises

to $8\%.$ What do you believe will be the percentage point change in the price per bond?