Way 2 Freshers

CONCEPT

Let rate=R%per annum, Time= T years

1.Present worth (PW) = (100*Amount)/(100+(R*T))

= (100* TrueDiscount)/(R*T)

2.TrueDiscount (TD) = (P.W*R*T)/100

= (Amount*R*T)/(100+(R*T))

3.Sum =(SimpeInterest*TrueDiscount)/(SimpleInterest-TrueDiscount)

4.SimpleInterest-TrueDiscount=SimpeInterest on TrueDiscount

5.When the sum is put at CompoundInterest,then

PresentWorth=Amount/(1+(R/100))^T

GeneralConcept:

Suppose a man has to pay Rs.156 after 4 years and the rate of interest is 14%per annum
Clearly ,Rs.100 at 14% will amount to Rs156 in 4 years So,the payment of Rs.100 now wil cear off the debt of Rs156 due 4 years hence We say that
Sum due = Rs156 due 4 years hence
Present Worth =Rs100
True Discount=Rs.156-Rs100=Rs56
=Sumdue-PW
We define
TrueDiscount= Interest on Present Worth(PW)
Amount = PresentWorth+TrueDiscount

SIMPLE PROBLEMS

1.Find the present worth of Rs.930 due 3 years hence at 8% pera nnum.Aso find the discount?

Sol: Amount=RS.930,Time=3years,Rate=8%

TrueDiscount = (Presentworth*Time*Rate)/100

Presentworth = (Amount*100) /(100+(R*T))

Presentworth = (930*100)/(100+(8*3)

=Rs.750

TrueDiscount = (930*3*8)/(100+(8*3)) =Rs.180 (or)

TrueDiscount = Amount-Presentworth

=Rs.930-Rs.750

=Rs.180

2.The truediscount on a bill due 9 months hence at 12% per annum is Rs540.Find the amount of the bill and its presentworth?

Sol: Time=9months=9/12years=3/4years

Rate=12%

TrueDiscount=Rs540

TrueDiscount=(Amount*100)/(100+(R*T))

=>Amount=(TrueDiscount*(100+(R*T))) /100

=(540*(100+12*(3/4))/100

=Rs.6540

Presentworth=Amount-TrueDiscount

=Rs.6540-Rs540

=Rs.6000

3.The TrueDiscount on a certain sum of money due 3 years hence is Rs.250 and SimpeInterest on the same sum for same time and same rate is Rs375 find sum and rate%?

Sol: Time=3 years

Truediscount=Rs.250

SimpeInterest=Rs375

Sum = (SimpeInterest*TrueDiscount)/(SimpeInterest-TrueDiscount)

= (375*250)/(375-250)
=Rs.750
SimpeInterest=(Principle*Time*Rate)/100
375 = ( 750*3R)/100
R=50/3%
=> Rate=162/3%

4.The difference between SimpeInterest and TrueDiscount on a certain sumof money for 6 months at 121/2% per annum is Rs25.find the sum.

Sol: Let amount be Rs.x
SimpleInterest=(Amount*T*R)/100
TrueDiscount=(Amount*T*R)/(100+(R*T))
SI-T.D=Rs25
=>((x*6/12*25/2)/100)-((x*6/12*25/2)/(100+(6/12*25/2))=25
=>x=Rs.6800

5.The Present worth of Rs.2310 due 21/2yrs henceThe interest being 15% per annum is
sol: Amount=Rs2310,Time=21/2yrs,Rate=15%

Presentworth = (Amount*100) /(100+(R*T))

=2310*100/(100+15*5/2)

=Rs1680.

MEDIUM PROBLEMS

1.A bill falls due in 1 year.The creditor agrees to accept immediate payment of the half and to defer the payment of the other half for 2 years .By this arrangement he gains Rs.40.what is the amount of bill,if the money be worth 121/2%?

sol: Let the amount be Rs.x
If the bill falls due for 1 yr,
Truediscount=(Amount*100)/(100+R*T)
=(x*100)/(100+(25/2*1)
If Accepting immediate payment of the half and to
defer the payment of the other half for 2 years,
Truediscount=(Amount*100)/(100+R*T)
=[x/2+((x/2*100)/(100+(25/2*2))]
x/2 for immediate payment,
((x/2*100)/(100+(25/2*2)) for paying after 2 yrs
He gains Rs40
=>[x/2+((x/2*100)/(100+(25/2*2))] – (x*100)/(100+(25/2*1) = Rs40
=> x/2+2x/5-8x/9=40
=>x=Rs.3600
Amount of the bill=Rs.3600

2.If the truediscount on a sum due 2yrs hence at 14% per annum be Rs168.The sum due is?
Sol: Time=2yrs,
Rate=14%
Truediscount=Rs168,Amount=x
TrueDiscount=(Amount*R*T)/(100+R*T)
168 =(x*14*2)/(100+(14*2))
=>x=Rs.768

3.The truediscount on Rs.2562 due 4 months hence is Rs.122.The rate % is?
Sol: Amount=Rs.2562
Time=4/12yrs
TrueDiscount=Rs122
Rate=X%

TrueDiscount=(Amount*R*T)/(100+R*T)
=>122=(2562*x*(4/12))/(100+(x*(4/12))
=>36600+122x=2562x
=>Rate=15%

4.The Truediscount on Rs1760 due after a certain time at 12% per annum is Rs160The time after which it is due is:
Sol: Amount=Rs.1760
Rate=12%
Truediscount=Rs160
Time=x
TrueDiscount=(Amount*R*T)/(100+R*T)
=>x*11*12=100+12x
=>x=5/6yr
Time=10months

5.The interest on Rs.760 for 2yrs is the same as theTruediscount on Rs960 due 2yrs hence .If the rate ofinterest is same in both cases,it is
sol:
Principal=Rs.760
Time=2yrs
amount=Rs960
P*T*R/100=(Amount*R*T)/(100+R*T)
=>(750*2*r)/100=(960*r*2)/(100+2r)
=>150r=2100
rate=14%

6.The SimpleInterest & TrueDiscount on a certain sum of money for a given time & at a given rate are Rs85 & Rs.80.The sum is………….
sol:
S.I= Rs.85
TrueDiscount=Rs80
Sum=(S.I.*TD)/(SI-T.D)
=Rs.1360

7.A trader owes a maerchant Rs10028 due 1yr hence The trader wants to settle the account after 3 months .If the rate of interest is 12%per annum How much cash should he pay?
Sol:
Time=1yr but he settles account after 3months
so time = 9months
Cash to pay=(Amount*R*T)/(100+R*T)
=(10028*100)/(100+12*(9/12))
=Rs.9200

8.A man buys a watch for Rs1950 in cash and sells it for Rs2200 at a credit of 1yrThe rate of interest is 10% per annum Then he gains / loose—————amount?
Sol:
If he sells it for Rs2200 at a credit of 1yr then the
present worth of that amount is
Presentworth = (Amount*100) /(100+(R*T))
=(2200*100)/(100+10*1)
=2000/-
So he gains 2000-1950=Rs.50

9.A owes Rs.1573 payable 11/2yrs hence ,Aso B owes A Rs.144450 payabe 6months hence If they want to settle the accunt forth with ,keeping 14% as the rate of interest ,then who should pay
& how much?
Sol:
B->A———–Amount=Rs.1573
Rate=14%
Time=3/2
Presentworth = (Amount*100) /(100+(R*T))
=(1573*100)/(100+(3/2)*14)
=Rs1300
A->B————Amount=Rs.1444.50
Rate=14%
Time=1/2
Presentworth = (Amount*100) /(100+(R*T))
=(1444.50*100)/(100+(1/2)*14)
=Rs1350
so B should pay Rs.1350

10.If Rs20 is the TrueDiscount on Rs260due after a certain time.What wil be trueDiscount on same sum due after ½ of former time,the rate of interest beng the same?
Sol:

Simple Interest on (260-20) for a gven time=Rs20
Simple Interest on (260-20) for a half time=Rs20*(1/2)
=Rs10
True Discount on Rs.250=Rs10
True Discount on Rs.260=Rs10*260/250
=Rs10.40

11.A has to pay Rs.220 to B after 1yr.B asks A to pay Rs.110 in cash and defer the payment of Rs,.110 for 2 yrs.A agrees to it.If the rate of interest be 10% per annum in this mode
of payment:…
………… sol:
A has to pay =Present worth of Rs220 due 1yr hence
=Rs.(220*100)/(100+(10*1))
=Rs.200 A actually pays=Rs.110+Presentworth of Rs110 due 2 yrs hence
=[110+ (Amount*100) /(100+(R*T))]
=[110+((110*100)/(100+(10*2)))]
=Rs192.66
So A gains Rs(200-192.66)=Rs.7.34