A bond has a maturity of $5$ years and a duration of $4\mathrm{.}465$ years. It pays an annual coupon at a coupon rate of $6\%$ and is trading at a price of $$100,$ implying a yield of $6\%.$ What is the estimated proportional change in price $($based on duration$)$ if the yield changes to $7\%?$

a$.4\mathrm{.}227\%$

b$.4\mathrm{.}212\%$

c$.-4\mathrm{.}212\%$

d$.-4\mathrm{.}227\%$

What is the estimated price after this change in yield $($based on duration$)?$

a$.$$$95\mathrm{.}788$

b$.$$$103\mathrm{.}512$

c$.$$$95\mathrm{.}088$

d$.$ $$104\mathrm{.}212$