Pr e mi u mo rdi sc o u n tEqu at i o n I nt h i ss e c t i o n ,wes h al ldi s c u s st h ep r o c e du r ei ns o l v i n gb o n dp r e mi u man db o n ddi s c o u n to na b o n dr e de e mab l eo rb o u g h tatp ar ,b o u g h tatap r e mi u m,o rb o u g h tatadi s c o u n t ,b yde t e r mi n i n gf i r s t t h ep u r c h as ep r i z e . T h ef o l l o wi n gf o r mu l aswi l lb eu s e di nt h i ss e c t i o n . Bo n dp r e mi u m( Pb) ( ) ) ( 1 1 +i Pb=Rv( b–i ) i Bo n ddi sc o u n t( Db) ( ) ) ( 1 +i 1 Db=Rv( i–b ) i Pu r c h asep r i c e Bo u g h tatap r e mi u m p=Rv+Pb Bo u g h tatadi sc o u n t p=Rv–Db I l l u s t r at i v eEx amp l e s : Ex amp l e1 : Fi n dt h ep u r c h as ep r i c ean ddi s c o u n to fa1 6%,m=4,P50, 000b o n dmat u r i n gi n1 5%t oy i e l d t h eb u y e r1 6. 5%c o mp o u n dqu ar t e r l yan dr e de e mab l eatp ar . So l u t i o n : Gi v e n :Fv=P50, 000=R j =1 00%=1 . 00 n =4( 1 5)=60 r =1 6%=0. 1 6 b t =1 5y e ar s y =1 6. 5%=0. 1 65 m=4 0. 1 6 b = =0. 04 4 0. 1 65 i = = 0. 041 25 4 Re qu i r e d: p u r c h as ep r i c epan db o n ddi s c o u n tDb. Fo r mu l a: Db=Rv( i–b ) ( ) ) ( 1 1 +1 i p=Rv–Db Co mp u t at i o n s : ) ( 1 ( 1 +0. 041 25 Db=50, 000( 0. 041 25–0. 04) 0. 041 25 ) ( 0. 91 1 5497 35 Db=50, 000( 0. 001 25) =50, 000( 0. 001 25)( 22. 0981 7 541 ) 0. 041 25 Db=P1 , 381 . 1 4 p=50, 000=1 , 381 . 1 4=P48, 61 8. 86 T h u s ,t h ep u r c h as ep r i c eo ft h eb o n di sP48,61 8. 86an dt h eb o n ddi s c o u n ti sP1 , 381 . 1 4. Ex amp l e2: AP36, 000b o n dwi t hi n t e r e s tat1 5%p ay ab l es e mi an n u al l yi sp r i c e dt oy i e l d1 2%,m=2.Fi n d t h ep r e mi u man dt h ev al u eo ft h eb o n d.I fi ti sr e de e mab l eatp aratt h ee n do ft e ny e ar san ds i x mo n t h s . So l u t i o n : Gi v e n : Fv=P36, 000=Rv j=1 00%=1 . 00 r 5%=0. 1 5 b=1 t=1 0. 5y e ar s y=1 2%=0. 1 2 m =2 0. 1 5 b= =0. 07 5 2 n=2( 1 0. 5)=21 Re qu i r e d: p u r c h as ep r i c epan db o n dp r e mi u mPb. Fo r mu l a: Pb=Rv( b–i ) Co mp u t at i o n s : Pb=36, 000( 0. 07 5–0. 06) ( ) ) ( 1 1 +i i p=Pv+Rb ) ( ( Pb=36, 000( 0. 01 5) Pb=P6, 352. 60 0. 1 2 i= =0. 06 2 ( 1 +0. 06) 1 0. 06 ) 0. 7 05644597 =36, 000( 0. 01 5)( 1 1 . 7 6407 662) 0. 06 p=36, 000+6, 352. 60=P42, 352. 60 T h u s ,t h ep u r c h as ep r i c eo ft h eb o n di sP42, 352. 60an dt h eb o n dp r e mi u mi sP6, 252. 60.