exercise no 8 bcom business math punjab university

8/19/2019 Exercise No 8 BCOM Business Math Punjab University

1/26

Exercise No: 7 Percentages Permutation & Combination

(7.1)

Express as percents:

(i)

1

2 = 0.5 x 100 = 50%

(ii)3

5 = 0.6 x 100 = 60%

(iii)3

25 = 0.12 x 100 = 12%

(iv) 1

1

2 = 3/2 = 1.5 x 100 = 150%

(v) 2

1

4 = 9/4 = 2.25 x 100 = 225%

(vi)1

50 = 0.02 x100 = 2%

(vii)8

10 = 0.8 x 100 = 80%

(viii)1

4 = 0.25 x 100 = 25%

(7.2)

Express the eci!a"s as percents:

(i) 0.25 = 0.25 x 100 = 25%

(ii) 0.06 = 0.06 x 100 = 6

(iii) 0.89 = 0.89 x 100 = 89%

(iv) 0.17 = 0.17 x 100 = 17%

(7.3)

Express #$""$in& percents as #racti$ns:

(i) 50% =50100 =

12

(ii) 25% =25

100 =1

4

Prepared & Selected By Iftikhar Ali Msc Economics (AI!)" #erti$cation in #hinese %istory & PoliticalEconomy %oard !ni'ersity" Beha'ioral Economics (oronto !ni'ersity)" lo*ali+ation (%oard!ni'ersity)" American #apitalism (#ornell !ni'ersity)" St,dent of #MA (#erti$ed Mana-ementAcco,ntant) Instit,te of #ost & Mana-ement Acco,ntancy Pakistan. eachin- at P,na* #olle-e of e/cellence in #ommerce 0amra #antt


2/26

(iii) 16% =16

100 =4

25

(iv) 230% =230

100 =23

10

(v) 871

2

% =175

2 x

1

100 =

175

200 =

7

8

(vi) 20% =20

100 =1

5

(vii) 4% =4

100 =1

25

(viii) 99% =99

100

(7.4)

Express these percents as eci!a"s:

(i) 15% =15

100 = 0.15

(ii) 85% =85

100 = 0.85

(iii) 121

2 % =25

2 '1

100 =25

200 = 0.125

(iv) 61

4 % =25

4 '1

100 =25

400 = 0.625

(7.5)

in:

(a) 5% $# 200 = ase x *eci!a" +ate = 200 ' 0.05 = 10

(,) 6% $# 180 = ase x *eci!a" +ate = 180 ' 0.06 = 10.8

(c) 12% $# 15 = ase x *eci!a" +ate = 15 ' 0.12 = 1.80

() 23% $# 4500 = ase x *eci!a" +ate = 4500 ' 0.23 = 1035



3/26

(e) 85% $# 400 = ase x *eci!a" +ate = 400 ' 0.85 = 340

(#)3

4 % $# 2000 = ase x *eci!a" +ate = 2000 ' 0.75 = 1500

(7.6)

-hat percent $# the sec$n n!,er is the #irst n!,er

(i) 40 80 = ercenta&e% = Number

Base =40

80 = 0.5 = 0.5 ' 100 = 50%

(ii) 60 80 = ercenta&e% = Number

Base =60

80 = 0.75 = 0.75 ' 100 = 75%

(iii) 150 200 = ercenta&e% = Number

Base =150

200 = 0.75 = 0.75 ' 100 = 75%

(iv) 12 48 = ercenta&e% = Number

Base =12

48 = 0.25 = 0.25 ' 100 = 25%

(iv) 146 292 = ercenta&e% = Number

Base =146

292 = 0.5 = 0.5 ' 100 = 50%

(v) 24 96 = ercenta&e% = Number

Base =24

96 = 0.25 = 0.25 ' 100 = 25%

(7.7)

# 5% $# a n!,er is 60 hat is the n!,er

!,er = Percentage of Number (100)

Rate =60 (100)

5 =6000

5 = 1200

(7.8)

#12 % $# a n!,er is 82.46 hat is the n!,er


Rate =82.46(100)

1/2 =8246

0.5 = 16492



4/26

(7.9)

# 45% $# n!,er is 3000 hat is the n!,er


Rate =3000 (100)

45 =300000

45 = 6666.67

(7.10)

# 4.6% $# a n!,er is 460 hat is the n!,er


Rate =460(100)

4.6 =46000

4.6 = 10000

(7.11)

If 0.2% of a number is 1467.24, what is the number?


Rate =1467.24 (100)

2 =146724

2 = 7336.35

(7.12)

r. ha"i ,$&ht a rai$ #$r +s. 1200 an he s$" it #$r +s. 1425. in his percent pr$#it.

Profit = Selling Prie ! "ost Prie = 142# ! 1200 = 22# so 22# is our number an$ 1200 is base. ow &ut

the &erentage formula whih is below'

ercenta&e% = Number

Base =225

1200 = 0.1875 = 0.1875 x 100 = 18.75%

(7.13)

r. $$r ha!!a &ets 15% pr$#it #r$! his invest!ent. e &ets +s.400 as net pr$#it #in his

invest!ent.

nvest!ent = Percentage of Profit (100)

Rate =400(100)

15 =40000

15 = 2666.67



5/26

(7.14)

# 7% $# the a!$nt is +s.490. in the a!$nt.

$ta" !$nt = Percentage of Amount (100)

Rate =490(100)

7 =49000

7 = 7000

(7.15)

he se""in& price $# a stee" ca,inet is +s. 840 an the &r$ss pr$#it is 10% $# the c$st. in the c$st.

It means that ost ( &rofit both are inlu$e$ in selling &rie so if selling &rie is )40 an$ &rofit is 10%,

then'

840

110 = 7.6*7 so ost &rie will be 7.6*7 + 100 = 76*.7

(7.16)

in the se""in& price $# tperiter hich c$sts +s. 4000 an the !ar; p is 8%.

100% ost &rie of t&ewriter is 4000 if there is )% mar- u& then total selling &rie will be'

Selling &rie =4000

100 + 10) = 40 + 10) = 4*20

(7.17)

!an s$" a #$ntain pen #$r +s. 125. is pr$#it as 30% $# his $ri&ina" prchase price. -hat ashis prchase price

Selling &rie = 12#, is &rofit is inlu$e$ in selling &rie whih is *0%, so his &urhase &rie will be'

Purhase &rie =125

130 + 100 = 0./616 + 100 = /6.16

(7.18)

in the se""in& price $# a piece $# #rnitre h$se c$st $# pr$cti$n is +s. 1400 an percenta&e

!ar; p is 35%. -hat is the a!$nt $# pr$#it

If ost of &ro$ution is 1400 an$ mar- u& is *#% aboe the ost then selling &rie will be'

Selling Prie =1400

100 + 1*# = 14 + 1*# = 1)/0



6/26

Profit = selling &rie ! ost &rie = 1)/0 ! 1400 = 4/0

(7.19)

hat is the ost of olore$ S3 5? Set whih is sol$ for s. /)00, if the &erent mar-u& is 40% on

ost.

$""$ a,$ve


7/26

>et the t$ta" pr$#it = 100

gets #0% =50

100 + 100 = s #0

; gets *0% of remaining = 8100 ! #090.*0 = #0 80.*09 = s 1#

" gets 60% of the balane = 8100 ! #0 ! 1#90.60 = *# 80.609 = s 21

emaining amount = 8100 ! #0 ! 1# ! 219 = s 14 $ii$e$ euall = 14>* = s 4.67 for eah

s " gets s 21 then total amount he gets = 21 4.67 = 2#.67If " gets s 1#0 then total &rofit will be'

otal &rofit =150 (100)25.67 = #)4.*4

(7.25)

an @ are in partnership. &ets 40% $# the t$ta" pr$#it 50% $# the re!ainin& pr$#it an @

80% $# the ,a"ance. n a!$nt "e#t $t is e


8/26

Aar-et Prie of a a$io Set =555

92.5 + 100 = 600

(7.29)

@har traers ea"in& &enera" &$$s s$" the #$""$in& artic"es t$ a cst$!er r. ha"i.

(a) $er i,et s!a"" 3 $Bens C+s. 84 per $Ben.

(,) $er $ns s!a"" 5 $Bens C+s. 60 $Ben.(c) "ac; +$se hair c$"$r 25 ,$tt"es C+s. 20 per ,$tt"e.

() >ipstic; 30 pieces C+s. 10 per piece.

(e) air pins 20 $Bens C+s.5 er $Bens.

r. ha"i as a""$e 71

2 % trae isc$nt. in the net a!$nt paa,"e t$ char

traers.

Bollow the aboe Cuestion of ra$e $isount

(7.30)

+aDa @$rp$rati$n prchase cc"es $rth +s. 11400 #r$! han @c"e At$re. e sett"e his acc$nt

a#ter ectin& 6% cash isc$nt. in the net a!$nt pai t$ han @c"e At$re.

Sim&l ta-e 6% on 11400 an$ $e$ut it from the &urhase &rie

(7.31)

n the prchase $# a car the ea"er a""$e t$ a cst$!er isc$nt at the rate $# 41

2 % . in $t

the t$ta" price $# a car an a!$nt pai t$ ea"er i# the isc$nt a""$e as +s. 6000.

Same as aboe

(7.32)

n i!p$rter ,s &$$s at 20% isc$nt ,t an i!p$rt t at 20% $n the c$st. # the $ther expenses

a!$nt t$ 5% $# the "ane c$st , h$ !ch percent sh$" ,e &$$s he !ar;e a,$ve "ist price s$

as t$ &ain 20% $n the t$ta" c$st.

Det the list &rie = s 100@isount = s 20

"ost Prie = s )0

@ut on "ost at the rate of 20% = )0 80.209 = s 16Dan$e$ Prie = )0 16 = s /6



9/26

E+&enses at #% on lan$e$ &rie = /6 80.0#9 = s 4.)0

otal "ost = /6 4.)0 = s 100.)0

Profit 20% at total ost = 100.)0 80.209 = s 20.16Selling Prie = 120./6 in whih Dist &rie is s 100 an$ @ifferene is 20./6

(7.33)

!erchant in >ah$re ,s s$!e rai$ sets #r$! arachi @$. he cata"$&e price $# hich is +s. 600

per set. he trae isc$nt a""$e t$ hi! , the arachi @$!pan is. 15% $n the cata"$&e price.

he #rei&ht an $ther char&es a!$nt t$ 21

2 % $# the cata"$&e price. he >ah$re !erchant se""s

each set at 10% isc$nt $n his "ist price $# +s. 750 ths !a;in& a net pr$#it $# +s. 1350. in the

n!,er $# rai$ sets ,$&ht.

"atalogue Prie of ra$io sets = 600

ra$e $isount 1#% = 600 80.1#9 = /0"atalogue &rie after $e$uting tra$e $isount = 600 ! /0 = #10

Breight ( other harges at the rate of 2.#% on atalogue &rie = 600 80.02#9 = 1#

otal "ost = #10 1# = #2#

Dist Prie of a set = 7#0@isount at the rate of 10% = 7#0 80.109 = 7#

Dist Prie after $e$uting $isount = 7#0 ! 7# = 67#

Profit for eah set = list &rie &er set ! total ost &er set = 67# ! #2# = 1#0 umber of sets he bought = otal &rofit>Profit &er set = 1*#0>1#0 = / sets

(7.34)

Fshirt !ar;e at +s. 145 as s$" #$r +s. 100 in a c"earance sa"e. in the rate $# isc$nt.

ate of @isount =145−100

145 + 100 =

45

145 + 100 = *1.0*4

(7.35)

#rnitre ea"er pai +s. 10000 #$r 50 "an chairs $n hich he ha ,een &iven isc$nt $# 12%.

in the price $# a "an chair.

Per "hair Prie after $e$uting 12% $isount =10000

50 = 200 Per "hair

Prie &er hair before $e$uting 12% $isount =

200

88 + 100 = 227.2727

(7.36)

r. Gah$$r a""$s 10% trae isc$nt an 3% cash isc$nt. in the net a!$nt t$ the c$st #in $t

the c$st price $# the air c$$"er.Prepared & Selected By Iftikhar Ali Msc Economics (AI!)" #erti$cation in #hinese %istory & PoliticalEconomy %oard !ni'ersity" Beha'ioral Economics (oronto !ni'ersity)" lo*ali+ation (%oard!ni'ersity)" American #apitalism (#ornell !ni'ersity)" St,dent of #MA (#erti$ed Mana-ementAcco,ntant) Instit,te of #ost & Mana-ement Acco,ntancy Pakistan. eachin- at P,na* #olle-e of e/cellence in #ommerce 0amra #antt


10/26

@ata is missing

(7.37)

n air c$$"er !ar;e at +s. 5000. trae a""$s a isc$nt $# 4%. # he sti"" &ains 10% $n the c$st

#in $t the c$st price $# the air c$$"er.

Same as aboe

(7.38)

pr$pert chan&e hans three ti!es an at each ti!e the "$ss t$ the se""er as 10%. # in the "ast

transacti$n the "$ss as +s. 405 #in $t the $ri&ina" va"e $# the pr$pert.

Det the &rie of &ro&ert = 100

Doss in first selling = 100 80.109 = 10Doss in seon$ selling = /0 80.109 = / where /0 = 8100 ! 109

Doss in thir$ time selling = )1 80.109 = ).10

If loss is 40# in last transation the original &rie is =405(100)

8.10 = #000

(7.39)

car chan&e hans three ti!es an at each ti!e the pr$#it t$ the se""er as 8%. # in the "ast

transacti$n the pr$#it as +s. 5000 #in the $ri&ina" price $# car.

Same as aboe

(7.40)

h$se as s$" #$r +s. 78350. he pr$pert ea"er as a""$e a c$!!issi$n $# 2%. in $t his

c$!!issi$n.

Same as aboe

(7.41)

c$!!issi$n a&ent entit"e a c$!!issi$n $# 61

4 % $n the &r$ss sa"e. in $t his c$!!issi$n i# he

s$" !erchanise #$r +s. 7425.

Sim&le Perentage

(7.42)

!erchant &ives his a&ent 10% $rinar c$!!issi$n p"s 3

1

3 % e"ereere $n the sa"e $# &$$s

$rth +s. 4260. $ !ch $es he receive a#ter pain& the a&ents re!nerati$n

Sim&le Perentage

(7.43)



11/26

c$!!issi$n a&ent entit"e a c$!!issi$n $# 8% $n t$ta" sa"es !ae , hi! p"s a ,$ns1

4 % $n

the excess $# his sa"es $ver +s. 10000. # his inc$!e is +s. 1250 #in the va"e $# the &$$s s$" , hi!.

otal Inome = 12#0 in whih'

)% ommission on amount 10000 = 1000080.0)9 = )00;onus "ommission = 12#0 ! )00= 4#0

n eer e+tra 100 s sales agent reeies )% &lus F% = ).2#% &ortion of ommission of total amount

whih means that 4#0 s is a ).2# &ortion of 100 &erent so the total e+tra amount will be'

E+tra amount of sales =450

8.25 + 100 = #4##

otal Sales = 10000 #4## = 1#4##

(7.44)

sa"es!an is pai a sa"ar $# +s. 500 a !$nth an 1% c$!!issi$n $n sa"es. # his t$ta" inc$!e in $ne

!$nth is +s. 750 #in the va"e $# his sa"es in that !$nth.

otal Inome = 7#0 in whih'Aonthl Salar mount = #00

"ommission mount = 7#0 ! #00 = 2#0 whih is 1% of sales then 100% amount of sales will be'

otal Sales =250

1 + 100 = 2#000

(7.45)

sa"es!an is pai a sa"ar $# +s. 1800 a !$nth an 2% $n sa"es $r $n" a c$!!issi$n $# 61

2 % $n

sa"es. # in $ne !$nth his inc$!e ner ,$th a"ternatives is sa!e #in $t the va"e $# his sa"es in that

!$nth.

61

2 of sales = 1)00 2% of sales

61

2 + ! 2+ = 1)00 G 41

2 += 1)00 G9

2 += 1)00 G 4.#+ = 1)00 G + =1800

4.5

G + = 400

otal 5alue of Sales = 400 + 100 = 40000

(7.46)

t 5% rate $# c$!!issi$n iss e"s$n a sa"es &ir" &$t +s. 250 $n the sa"e $# ta"c! #ace p$er. in

the va"e $# her sa"es. # the price $# #ace p$er as +s. 2.50 per c$ntainer h$ !an c$ntainers i

she se""



12/26

otal sales =250

5 + 100 = #000

otal "ontainers at 2.#0 &er ontainer =5000

2.5 = 2000 "ontainers

(7.47)

in the t$ta" a!$nt $# c$!!issi$n $n sa"e t$ +s. 8000 i# the c$!!issi$n rate is 8%.Sim&le Perentage

(7.48)

,siness!an instrct the a&ent t$ , 50 cc"es at +s. 1200 per cc"e an t$ se"" the! at +s. 1325 each.

# a&ent char&e 2% c$!!issi$n $n the prchase an 2% $n sa"es. in the t$ta" c$!!issi$n $n

prchase an sa"e. "s$ #in the a!$nt $# pr$#it !ae , ,siness!an.

Purhase Prie of "les = 1200 + #0 = 60000"ommission on Purhase Prie = 6000080.029 = 1200

Sales Prie of "les = 1*2# + #0 = 662#0

"ommission on Sale Prie = 662#080.029 = 1*2#otal "ommission = 1200 1*2# = 2#2#

Profit = @ifferene between Sale ( Purhase Prie ! otal "ommission

Profit = 8662#0 ! 600009 ! 2#2# = 62#0 ! 2#2# = *72#

(7.49)

r. Gia ssain a""$e the sa"es!an 6% c$!!issi$n $n t$ta" sa"es !ae , hi! p"s a ,$ns3

4

% $n the excess $# his sa"es $ver +s. 10000. # his t$ta" earnin&s are +s. 1140. in the va"e $# the

&$$s s$" , hi!.

6% "ommission on 10000 = 1000080.069 600"ommission on e+tra sale = 1140 ! 600 = #40

s we -now that #40 is 6% &lus 0.7#% total 6.7#% of e+tra sales then e+tra sales will be'

Sales aboe 10000 =

540

6.75 + 100 = )000

otal Sales = 10000 )000 = 1)000

(7.50)

n 1990 a sa"es!an as pai 5% c$!!issi$n $n sa"es. n 1991 the rate as increase t$ 6% an his

sa"es a"s$ increase , +s. 2000. # his re!nerati$n in 1991 exceee that 1990 , +s. 220 #in $t

the va"e $# &$$s s$" , hi! in each ear.

6% ommission on inrease$ sale = 200080.069 = 120

1% on sale of 1//0 = un-nown

;oth ommission are = 220

120 1% on sale of 1//0 = 2201% on sale of 1//0 = 220 ! 120 = 100

If 1% ommission on sale is = 100 then total sales of 1//0 = 100 + 100 = 10000Sales of 1//1 = Sale of 1//0 Inrease$ Sale of 2000 = 10000 2000 = 12000



13/26

Exercise No: 8

(8.1)

in the si!p"e interest an a!$nt #$r the #$""$in&:

(i) +s. 2000 #$r 3 ears at 5%.

(ii) +s. 800 #$r 7 ears at 4%.

(iii) +s. 4000 #$r 5 ears at 6%.

A$"ti$n

(i) nterest = P x r x t

100 =2000 x 5 x 3

100 =30000

100 = 300

(ii) Aa!e as a,$ve

(iii) Aa!e as a,$ve

(8.2)

$ !ch !$ne i"" a!$nt t$ +s. 900 in 4 ears at 7%Aa!e as a,$ve

(8.3)

in the interest an a!$nt #$r +s. 2000 #$r 3 !$nths at 6%.

Aa!e as a,$ve

(8.4)

r. s&har ,$rr$e +s. 5000 #$r 5 ears at 8% si!p"e interest. $ !ch he i"" repa

Aa!e as a,$ve

(8.5)

@a"c"ate the si!p"e interest $n +s. 11000 #$r 7 ears at 41

2 %.

(iv) nterest = P x r x t

100 =11000 x 4.5 x7

100 =346500

100 = 3465

(8.6)



14/26

r. ashir h!a ,$rr$e +s. 4500 #r$! a,i, an; at 81

2 an "ent the h$"e a!$nt at 10 %

the sa!e a hat $" he &aine #r$! this a#ter 4 ears.

Aa!e as a,$ve

(8.7)

ha"i ah!$$ ,$rr$e +s. 2500 #r$! A"tan #$r 31

2 ears at si!p"e interest at 8 % per

ann!. $ !ch ha"i ah!$$ has t$ pa at the en $# the peri$.

Aa!e as a,$ve

(8.8)

-hat s! $" ,$rr$ in +s. 1250 as si!p"e interest at 3 % in 3 ears

rincipa" = I x100

r x t =1250 x100

3 x 3 =125000

9 = 13889

(8.9)

in the principa" i# the a!$nt #$r 5 ears at 5% is +s. 5550.

rincipa" =

A x100

100+(r x t ) =

5550 x 100

100+(5 x5) =

555000

125 = 4440

(8.10)

$ !ch sh$" r. ri# ,$rr$ #r$! r. ani# s$ that he !a have t$ repa +s. 4425 a#ter 3 ears

i# ani# char&es a si!p"e interest rate 5%

Same as uestion )./

(8.11)

$ !ch sh$" r. a


15/26

rincipa" =

A x100

100+(r x t ) =2775 x100

100+(4 x 5.75) =277500

123 = 2256.09

(8.13)

-hat s! $# !$ne pt $t at si!p"e interest $" ,ec$!e +s. 420 in 22

3 ears at 41

2 %

rincipa" = I x100

r x t =420 x100

9/2 x 8/3 =42000

12 = 3500

(8.14)

t hat rate $# interest $" +s. 1800 a!$nt t$ +s. 2500 in 2 ears.

$ta" a!$nt $# interest #$r t$ ears = !$nt ? rincipa" = 2500 ? 1800 = 700

+ate $# nterest r = I x100

P x t =700 x100

1800 x 2 =70000

3600 = 19.45%

(8.15)

in the rate percent $# interest i# the si!p"e interest $n +s. 21540 #$r 4 ears an 9 !$nths is +s.

5000.

+ate $# nterest r = I x100

P x t =5000 x100

21540 x19 /4 = 5000 x100 x 421540 x19 = 4.89%

(8.16)

t hat rate $# interest $" a s! $# !$ne ,ec$!es $ne an a ha"# in 10 ears.

Det the sum = 100If I interest beomes one an$ half amount will beome after 10 ears = 1#0

So I = #0, = 1#0, Prini&al = 100, t = 10 then rate will be'

ate of Interest r = I x100

P x t =50 x100

100 x10 =

5000

1000 = #%

(8.17)

$ "$n& i"" it ta;e #$r +s. 1000 t$ a!$nt +s. 1180 at 6% per ann! si!p"e interest.

rincipa" = 1000 !$nt = 1180 = ? = 1180 ? 1000 = 180 r = 6 then t i"" ,e:



16/26

ime t = I x100

P+r =180 x100

1000 x6 =18000

6000 = * 3ears

(8.18)

# the si!p"e interest $n +s. 7500 at 51

2 % ,e +s. 1680 #in the ti!e.

Same as aboe(8.19)

n hat ti!e $" the si!p"e interest $n +s. 20000 ,e +s. 4000 at 31

3 %

Same as aboe

(8.20)

n h$ !an ears $" a s! "ent at 8% ,e $,"e

>et the principa" = 100 # a#ter the ti!e !$nt i"" ,e $,"e than = 200 = 200 ? 100 = 100

r = 8 then ti!e i"" ,e:

ime t = I x100

P+r =100 x100

100 x 8 =10000

800 = 12.# 3ears

(8.21)

in the c$!p$n interest $n +s. 8000 #$r 3 ears at 5% per ann!.

Prini&al mount P = )000, r = #, n = *

mount = P [1+ r

100 ] H = )000 [1+ 5

100 ] = )000 [105100 ] = )00081.0#9 = /261

"om&oun$ Interest = ! P = /261 ! )000 = 1261

(8.22)

in the a!$nt at c$!p$n interest $# +s. 12000 at 6% per ann! #$r 2 ears an 6 !$nths. "s$

#in the c$!p$n interest.

Prini&al P = 12000, If t is 2 ears an$ 6 months then its semi annuall an$ it will be n = # then r = *

mount = P [1+ r100 ] H = 12000 [1+ 3

100 ] # "alulate(8.23)

in the a!$nt $# +s. 10000 #$r 2 ears at:

(a) @$!p$ne anna"".

(,) @$!p$ne se!i anna"".



17/26

(c) @$!p$ne


18/26

in the principa" $# +s. 9628.20 e at the en $# 8 ears i# !$ne is $rth 6% c$!p$ne se!i

anna"".

mount = /62).20, n = )+2=16 beause of semi annuall, r = * beause of semi annuall

P= [ A

(1+ r

100)ⁿ ] G P= [

9628.20

(1+ 3

100)16 ] G P= [ 9628.20(1.03)16 ]

Det + = 81.0*916

a-ing log of both si$es log + = 16 log of 81.0*9 G log + = 16 80.012)*72249

Dog + = 0.20#*/##)4 a-ing antilog of both si$es G + = 1.604706*/7

So P = [ 9628.201.604706397 ] = 6000(8.29)

he c$!p$n interest #$r 5 ears at 5% is +s. 1000. in the principa".

>et App$se = 100 n = 5 r = 5 then i"" ,e:

mount = P [1+ r100 ] H = 100 [1+ 5

100 ] 5 = 100 (1.05) p$er5 = 100 (1.276281563) = 127.7281563@$!p$n nterest = ? = 127.7281563 ? 100 = 27. 7281563 then

P = [ 100 x C . I Assumed C . I ] = [ 100 x 100027.7281563 ] = [ 10000027.7281563 ] = *606

(8.30)

n h$ !an ears a s! $# +s. 1000 $" a!$nt +s. 1350 at 4% c$!p$ne interest.

= 1000 = 1350 r = 4% n =

n= [ logA−log P

log(1+ r

100) ]

@a"c"ate

(8.31)

n h$ !an ears a s! $# +s. 5560 $" a!$nt +s. 7000 at 8% interest c$!p$ne se!i

anna"".

= 5560 = 7000 r = 8% se!i anna"" 4% n =



19/26

n = [ logA−log P

log(1+ r

100) ] @a"c"ate

(8.32)

t hat rate $# interest c$!p$ne per ann! #$r 5 ears i"" +s. 2000 a!$nt t$ +s. 2550

P = 2000, = 2##0, n = #, r =?

[ r100 ] = ntilog P

log A−log ¿1

n ¿−1

¿

[ r

100

] = ntilog

P

log A−log ¿¿

¿ – 1¿¿

[ r100 ] = ntilog2000

log2550−log¿¿

¿−1¿¿

[ r

100 ] = ntilog

[3.40654−3.30103

5 ]−1

[ r100 ] = ntilog [0.10551

5 ]−1

[ r100 ] = ntilog 80.0211029 ! 1

[

r

100

] = 1.04/7))/#7 ! 1

[ r100 ] = 0.04/7))/#7r = 0.04/7))/#7 + 100Prepared & Selected By Iftikhar Ali Msc Economics (AI!)" #erti$cation in #hinese %istory & PoliticalEconomy %oard !ni'ersity" Beha'ioral Economics (oronto !ni'ersity)" lo*ali+ation (%oard!ni'ersity)" American #apitalism (#ornell !ni'ersity)" St,dent of #MA (#erti$ed Mana-ementAcco,ntant) Instit,te of #ost & Mana-ement Acco,ntancy Pakistan. eachin- at P,na* #olle-e of e/cellence in #ommerce 0amra #antt


20/26

r = 4./7))/#7 or #%

(8.33)

t hat rate $# interest c$!p$ne


21/26

Bor Sim&le Interest Interest I = P x r x t

100

Bor "om&oun$ Interest mount = P [1+ r100 ] H

(8.36)

# the i##erence ,eteen the si!p"e an c$!p$n interest #$r 3 ears at 5% is +s. 61. in the

principa".

Det Su&&ose P = 100, r = #, t or n = *

Sim&le Interest Interest I = P x r x t

100 = Interest I =100 x5 x 3

100 =1500

100 = 1#

"om&oun$ Interest mount = P [1+ r100 ] H = = 100 [1+ 5100 ] &ower *

= 100 81.0#9= 11#.762#

"om&oun$ Interest = ! P = 11#.762# ! 100 = 1#.762#

@ifferene between "om&oun$ ( Sim&le Interest = 1#.762# ! 1# = 0.762#

If $ifferene is 61 then the Prini&al will be'

P = [100 x610.7625 ] = )000

(8.37)

he i##erence ,eteen the si!p"e an c$!p$n interest $n a certain s! is +s. 2.50 #$r 2 ears at5%. in the s!.

Same as aboe

(8.38)



22/26

sum of mone was borrowe$ an$ &ai$ ba- in two eual annual installments of s. ))2, allowing #%

om&oun$e$ interest. hat was the sum borrowe$.

(8.39)

Kot. "ollege Baisalaba$ ha$ *000 stu$ents on 10th @eember, 1/70. If the number of stu$ents inreases at aom&oun$ rate of )% eer ear what shoul$ be the number of stu$ents in the ollege on 10th @eember,

1/)#.

(8.40)

Bin$ the alue of a t&e writer osting s. 1700 at the en$ of # ears, if $e&reiation at 4% &er annum.

(8.41)

mahine in shoes fator is &urhase$ for s. )#00. fter ) ears useful life its sra& will be s. *000.Bin$ the $e&reiation rate.

(8.42)

he mahiner in a fator is &urhase$ for s. #0000. ate of $e&reiation is 6%. fter how man ears, itsalue will be s. 20000.

Exercise No: 9

(9.1)

s. #00 a ear for ten ears at 4% om&oun$e$ annuall.

(9.2)

s. )00 a uarter for # ears at 4% om&oun$e$ uarterl.

(9.3)

s. 100 a month for # ears at 6% om&oun$e$ monthl.

(9.4)

man inests s. *00 at the en$ of eah month in a fun$ whih &as 4% om&oun$e$ semi< annuall. ow

muh $oes he hae Lust after the tenth $e&osit.

(9.5)

Bin$ the amount of s. 2#0 ineste$ at the en$ of eah of # suessie ears at 6% interest om&oun$e$

annuall.(9.6)

Aiss asima sae$ s. #40 &er ear whih she $e&osite$ in a saing ban- at the en$ of eah ear. If the ban-

&ai$ 2% interest om&oun$e$ annuall on all $e&osits, what the amount on $e&osit at the en$ of 11 ears?



23/26

(9.7)

Ar. Mhali$ wishes to sae mone to ta-e a tri&. If he $e&osits s. 1#0 at the en$ of eah month for 24 monthsin an inestment that &as 12% om&oun$e$ monthl, how muh will he hae on $e&osit.

(9.8)

Bin$ the amount of an or$inar annuit of s. 4400 &er uarter for # ears at the rate of 16% &er annum

om&oun$e$ uarterl.

(9.9)

Ars. Mhurshi$ $e&osit s. #### at the en$ of eah si+ months for 4 ears an$ 6 months at 10% om&oun$e$semi< annuall. Bin$ the amount of the inestment.

(9.10)

Bin$ the aumulate$ alue of s. #000 ineste$ at the en$ of eah uarter ear for # ears at )%

om&oun$e$ uarterl.

(9.11)

man sets asi$e s. 200 at the beginning of eah ear towar$s a fun$ for his son:s ollege e$uation. If the

mone is ineste$ at 4% &er ear, how muh will he aumulate$ at the en$ of 10 ears?

(9.12)

If a &ament of s. #00 is ma$e to$a an$ a li-e &ament eah ear for # ears, how muh will be on $e&osit

at the en$ of 4 ears, if the interest rate is #% om&oun$e$ annuall.

(9.13)

ow muh mone woul$ be aumulate$ at the en$ of 2* ears b a man if he ineste$ s. *2# on the first

$a of eah ear at 4% interest om&oun$e$ annuall?

(9.14)

n his fift first birth$a an$ eah thir$ month thereafter, @r. abib Nllah ineste$ s. 47# at 4% interest

om&oun$e$ uarterl. t the en$ of his fift seen ear, what was the amount on $e&osit?

(9.15)

Ar. slam bought a S3 .5. b &aing s. *#0 eah month for 12 months, beginning from now. If mone

is worth 12% om&oun$e$ monthl, what was the selling &rie of the .5. on eah &ament?

(9.16)

Bin$ the amount of an annuit $ue of s. 200 &ai$ at the beginning of eah 6 month &erio$ for ) ears if the

interest rate is 6% om&oun$e$ semiannuall.

(9.17)



24/26

house is rente$ for s. /00 &er month, with eah month:s rent &aable in a$ane. If the interest rate is

12% om&oun$e$ monthl an$ the rent is $e&osite$ in an aount, what is the amount of rent for one ear?

(9.18)

Bin$ the &resent alue of an annuit of s. 100 &ai$ at the en$ of eah ear for 17 ears if the interest rate is7% om&oun$e$ annuall.

(9.19)

Bin$ the &resent alue of an annuit of s. 100 &ai$ at the en$ of eah ear for ) ears if the interest rate is

)% om&oun$e$ semiannuall.

(9.20)

man wishes to $e&osit enough mone to$a so that his son an with$raw s. 2#00 at the en$ of eah earfor ten ears. ow muh he $e&osit, if the interest rate is 6% om&oun$e$ annuall.

(9.21)

hat is the &resent alue of an annuit if the siOe of eah &ament is s. 2000 &aable at the en$ of eahuarter for eight ears at an interest rate of 7% om&oun$e$ uarterl?

(9.22)

hat is the &resent alue of an annuit of s. *00 &er ear if the first &ament is reeie$ to$a an$ earlfor a total of 10 onseutie &aments, an$ mone is worth #% interest om&oun$e$ annuall?

(9.23)

he amount of an annuit for 12 ears is s. )0000. hat woul$ be the siOe of the uarterl installment if

the interest rate is 12% om&oun$e$ uarterl?

(9.24)

Ar. mLa$ wants to aumulate s. 60000 in ) ears. e ma-es eual $e&osits at the en$ of eah 6 months inan aount. he rate of interest is )% om&oun$e$ semiannuall. Bin$ the alue of eah $e&osit.

(9.25)

Ar. Datif borrowe$ s. 200,000 from his frien$ to &urhase a ar. e &romise$ to &a ba- the loan in

semiannual eual installments in * ears with interest rate at )% om&oun$e$ semiannuall. If first &amentis start at the en$ of first si+ monthl &erio$s, what woul$ be the amount of eah installment?

(9.26)

ow man semi annuall &aments of s. 200 eah to in a ban- in the form of an or$inar annuit will

aumulate s. 6000 if the interest rate is )%.

(9.27)



25/26

he ash &rie of a ar is s. 1#0000. If the interest rate is 24% om&oun$e$ uarterl. ow man uarterl

&aments he will ta-e to &a off ar, when uarterl &aments of s. 1#000 are ma$e.

(9.28)

Ar. Nsman wants to $e&osit his saings of s. 4)000 in a ban-. he ban- offers )% interest om&oun$e$semi annuall. Bin$ the number of with$rawals, if he $raw s. 2400 at the en$ of eah si+ months.

(9.29)

Ar. ahi$ inests s. #40 at the en$ of eah month amounts to s. 12644 in 11

2 ear. Bin$ the nominal

rate of interest.

(9.30)

n annuit of s. ))00 &aable at the en$ of eah ear amounts to s. 120000 in 10 ears. Bin$ the interest

of the annuit.

(9.31)

he K "om&an is e+&ete$ to &a s. 4.0 eer si+ months on a share of its sto- what is the &resentalue of this sti- if mone is worth #% om&oun$e$ semi annuall?

(9.32)

Bin$ the &resent alue of a om&an:s sto-, whih is e+&ete$ to &a s. 200 eer three month, if mone is

worth 6% om&oun$e$ uarterl.



26/26

Prepared & Selected By Iftikhar Ali Msc Economics (AI!)" #erti$cation in #hinese %istory & PoliticalEconomy %oard !ni'ersity" Beha'ioral Economics (oronto !ni'ersity)" lo*ali+ation (%oard!ni'ersity)" American #apitalism (#ornell !ni'ersity)" St,dent of #MA (#erti$ed Mana-ementAcco,ntant) Instit,te of #ost & Mana-ement Acco,ntancy Pakistan. eachin- at P,na* #olle-e of

exercise no 8 bcom business math punjab university

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