True Discount Concept & Questions

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% perannum.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 sum of 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.