a$.$ A $6\%$ coupon bond paying interest annually has a modified duration of $10$ years, sells for $$800,$ and is priced at a yield to maturity of $8\%.$ If the YTM increases to $9\%,$ what is the predicted change in price based on the bond's duration?

b$.$ A $6\%$ coupon bond with semiannual coupons has a convexity $($in years$)$ of $120,$ sells for $80\%$ of par, and is priced at a yield to maturity of $8\%.$ If the YTM increases to $9\mathrm{.}5\%,$ what is the predicted contribution of convexity to the percentage change in price due to convexity?

c$.$ A bond with annual coupon payments has a coupon rate of $8\%,$ yield to maturity of $10\%,$ and Macaulay's duration of $9$ years. What is the bond's modified duration?

d$.$ When interest rates decline, the duration of a $30-$year bond selling at a premium:

$$ Increases.

$$ Decreases.

$$ Remains the same.

$$ Increases at first, then declines.

e$.$ If a bond manager swaps a bond for one that is identical in terms of coupon rate, maturity, and credit quality but offers a higher yield to maturity, the swap is:

$$ A substitution swap.

$$ An interest rate anticipation swap.

$$ A tax swap.

$$ An intermarket spread swap.

f$.$ Which bond has the longest duration?

$8-$year maturity, $6\%$ coupon

$8-$year maturity, $11\%$ coupon

$15-$year$-$maturity, $6\%$ coupon

$15-$year$-$maturity, $11\%$ coupon