Compute the price $($value$)$ and the duration of each of the following fixed$-$income claims. Assume that all bonds pay annual coupons and have par values of $$1,000.$ Assume that P$/$E ratios are computed using current price and expected earnings $($rather than current earnings$),$ and that all earnings and dividend values are annual values.

a$.$ A zero$-$coupon bond with $11$ years left until maturity and a YTM of $5\mathrm{.}25\%.$

b$.$ A $4-$year, $5\mathrm{.}5\%$ coupon bond with a YTM of $4\mathrm{.}5\%.$

c$.$ A perpetuity with an annual cash flow of $$125,000$ and a YTM of $7\mathrm{.}5\%.$