Please show all work and explain clearly through the equations. Answers are given.

Given an interest rate increase of $75$ bp $(0\mathrm{.}750\%),$ compute the i$)$ percentage price change and ii$)$ an

estimate of the percentage price change using modified duration $($the duration rule$),$ for each of

the four bonds in question #$31.$

a$.$ Bond A$.-7\mathrm{.}11\%$; $-7\mathrm{.}47\%$

b$.$ Bond B$.-5\mathrm{.}68\%$; $-5\mathrm{.}89\%$

c$.$ Bond C$.-4\mathrm{.}24\%$; $-4\mathrm{.}36\%$

d$.$ Bond D$.-2\mathrm{.}61\%$; $-2\mathrm{.}65\%$

Given an interest rate increase of $75bp(0\mathrm{.}750\%),$ compute the i$)$ percentage price change and ii$)$ an estimate of the percentage price change using modified duration $($the duration rule$),$ for each of the four bonds in question #$31.$

a$.$ Bond A$.-7\mathrm{.}11\%$;$-7\mathrm{.}47\%$

b$.$ Bond B$.-5\mathrm{.}68\%$;$-5\mathrm{.}89\%$

c$.$ Bond C$.-4\mathrm{.}24\%$;$-4\mathrm{.}36\%$

d$.$ Bond D$.-2\mathrm{.}61\%$;$-2\mathrm{.}65\%$