b$)$ Another of your friend, Sarah, is by nature 'conservative' and hence does not have a

high tolerance for risk. She wants to be certain that her money is safe and that it will

be available in three years' time when she plans to start a business.

"I want to get a better return than I can get on bank term deposits and, presently I am

thinking about bonds," she has told you.

You have a quick look on the NZDX website and find two $3\%($coupon rate$)10-$year

$($maturity$)$ bonds $-$ New Zealand Government bond with a yield to maturity of $4\mathrm{.}12\%$

and corporate bond issued by Spark New Zealand with a yield to maturity of $6\mathrm{.}76\%.$

You note that the two bonds have quite different yields to maturity while their coupon

rates and maturities are the same. Based on the definition of yield to maturity, explain

what the difference means about the prices of the two bonds relative to each other.

Also discuss some potential reasons why they are so different.