Numerical application for the bonds defined in question $6$ above. An investor considers putting $1,000,000$$ in one of the following $6$ bonds :

Bond A: Coupon $c=5\mathrm{.}0\%,$ life span $n=10$ years

Bond B: Coupon $c=5\mathrm{.}0\%,$ life span $n=15$ years

Bond C: Coupon $c=3\mathrm{.}5\%,$ life span $n=10$ years

Bond D : Coupon $c=3\mathrm{.}5\%,$ life span $n=15$ years

Bond $E$ : Coupon $c=0\mathrm{.}0\%,$ life span $n=10$ years

Bond $F$ : Coupon $c=0\mathrm{.}0\%,$ life span $n=15$ years

We provide below the unit prices of these bonds for different values of the interest rate $r$ between $3\mathrm{.}3\%$ and $5\mathrm{.}5\%,$ as obtained by applying the formula found in question $5$ above:

$\backslash$table$[[I,A,$B$,$C$,$D$,$B$,$P$],[0\mathrm{.}035,1\mathrm{.}12475,1\mathrm{.}17276,1\mathrm{.}00000,1\mathrm{.}00000,0\mathrm{.}70892,0\mathrm{.}59589],[0\mathrm{.}036,1\mathrm{.}11585,1\mathrm{.}16010,0\mathrm{.}99173,0\mathrm{.}98956,0\mathrm{.}70211,0\mathrm{.}58831],[0\mathrm{.}037,1\mathrm{.}10703,1\mathrm{.}14762,0\mathrm{.}98353,0\mathrm{.}97729,0\mathrm{.}69536,0\mathrm{.}57985],[0\mathrm{.}038,1\mathrm{.}09831,1\mathrm{.}13531,0\mathrm{.}97542,0\mathrm{.}96617,0\mathrm{.}68869,0\mathrm{.}57153],[0\mathrm{.}039,1\mathrm{.}08967,1\mathrm{.}12316,0\mathrm{.}96739,0\mathrm{.}95521,0\mathrm{.}68209,0\mathrm{.}56334],[0\mathrm{.}040,1\mathrm{.}08111,1\mathrm{.}11118,0\mathrm{.}95945,0\mathrm{.}94441,0\mathrm{.}67556,0\mathrm{.}55526],[0\mathrm{.}041,1\mathrm{.}07264,1\mathrm{.}09937,0\mathrm{.}95158,0\mathrm{.}93375,0\mathrm{.}66910,0\mathrm{.}54732],[0\mathrm{.}042,1\mathrm{.}06425,1\mathrm{.}08772,0\mathrm{.}94378,0\mathrm{.}92325,0\mathrm{.}66271,0\mathrm{.}53949],[0\mathrm{.}043,1\mathrm{.}05594,2\mathrm{.}07622,0\mathrm{.}93607,0\mathrm{.}97299,0\mathrm{.}65638,0\mathrm{.}53178],[0\mathrm{.}044,1\mathrm{.}04771,1\mathrm{.}06488,0\mathrm{.}92843,0\mathrm{.}90268,0\mathrm{.}65012,0\mathrm{.}52419],[0\mathrm{.}045,1\mathrm{.}03956,1\mathrm{.}05370,0\mathrm{.}92087,0\mathrm{.}89260,0\mathrm{.}64393,0\mathrm{.}51672],[0\mathrm{.}046,1\mathrm{.}03150,1\mathrm{.}04266,0\mathrm{.}91339,0\mathrm{.}88267,0\mathrm{.}63780,0\mathrm{.}50936],[0\mathrm{.}047,1\mathrm{.}02351,1\mathrm{.}03178,0\mathrm{.}90597,0\mathrm{.}87288,0\mathrm{.}63173,0\mathrm{.}50211],[0\mathrm{.}048,1\mathrm{.}01559,1\mathrm{.}02104,0\mathrm{.}89864,0\mathrm{.}86322,0\mathrm{.}62573,0\mathrm{.}49497],[0\mathrm{.}049,1\mathrm{.}00776,1\mathrm{.}01045,0\mathrm{.}89137,0\mathrm{.}85370,0\mathrm{.}61979,0\mathrm{.}48794],[0\mathrm{.}050,1\mathrm{.}00000,1\mathrm{.}00000,0\mathrm{.}88417,0\mathrm{.}84431,0\mathrm{.}61391,0\mathrm{.}48102],[0\mathrm{.}051,0\mathrm{.}99232,0\mathrm{.}98969,0\mathrm{.}87705,0\mathrm{.}83504,0\mathrm{.}60810,0\mathrm{.}47420],[0\mathrm{.}052,0\mathrm{.}98471,0\mathrm{.}97952,0\mathrm{.}87000,0\mathrm{.}82591,0\mathrm{.}60234,0\mathrm{.}46748]]$

We assume that the current value of the interest rate r is $4\mathrm{.}3\%.$ If the investor puts the entirety of his $1,000,000$$ in one of these bonds, which one should he select if following his purchase, the interest rate were to vary slightly, say move from $4\mathrm{.}3\%$ to $4\mathrm{.}2\%?$ What would be the profit or loss in each case?