The following table summarizes the yields to maturity on several$$ one$-$year, zero$-$coupon$$ securities: $($Note$$: The yields displayed in the table are annually compounded$$ yields.$)$

Security

Yield

$$Treasury

$3\mathrm{.}13\%$

$$AAA corporate

$3\mathrm{.}21\%$

$$BBB corporate

$4\mathrm{.}21\%$

$$B corporate

$4\mathrm{.}96\%$

a$.$ What is the price$($expressed as a percentage of the face$$ value$)$ of a$$ one$-$year, zero$-$coupon corporate bond with an AAA$$ rating?

b$.$ What is the credit spread on$$ AAA$-$rated corporate$$ bonds?

c$.$ What is the credit spread on$$ B$-$rated corporate$$ bonds?

d$.$ How does the credit spread change with the bond$$ rating? Why?