Compound Concept
Compound Interest:Sometimes it so happens that the borrower and the lender agree to fix up a certain unit of time ,say yearly or half-yearly or quarterly to settle the previous account.
In such cases ,the amount after the first unit of time becomes the principal for the 2nd unit ,the amount after second unit becomes the principal for the 3rd unit and so on.
After a specified period ,the difference between the amount and the money borrowed is called Compound Interest for that period.
Formulae:
Let principal=p,Rate=R% per annum Time=nyears
1.When interest is compounded Annually,
Amount=P[1+(R/100)]n
2.When interest is compounded Halfyearly,
Amount=P[1+((R/2)100)]2n
3.When interest is compounded Quaterly,
Amount=P[1+((R/4)100)]4n
4.When interest is compounded Annually,but time in fractions say 3 2/5 yrs
Amount=P[1+(R/100)]3[1+((2R/5)/100)]
5.When rates are different for different years R1%,R2%,R3% for 1st ,2nd ,
3rd yrs respectively
Amount=P[1+(R1/100)][1+(R2/100)][1+(R3/100)]
6.Present Worth of Rs.X due n years hence is given by
Present Worth=X/[1+(R/100)]n
SIMPLE PROBLEMS
1.Find CI on Rs.6250 at 16% per annum for 2yrs ,compounded annually.
Sol:
Rate R=16,n=2,Principle=Rs.6250
Method1:
Amount=P[1+(R/100)]n
=6250[1+(16/100)]2
=Rs.8410
C.I=Amount-P
=8410-6250
=Rs.2160
Method2:
Iyear------------------6250+1000
\\Interest for 1st yr on 6250
II yr---------------6250+1000+160
\\Interest for I1yr on 1000
C.I.=1000+1000+160
=Rs.2160
2.Find C.I on Rs.16000 at 20% per annum for 9 months compounded quaterly
Sol:
MethodI:
R=20%
12months------------------------20%
=> 3 months------------------------5%
For 9 months,there are '3' 3months
--------16000+800
--------16000+800+40
--------16000+800+40+10+2
=>Rs.2522
MethodII:
Amount=P[1+(R/100)]n
=16000[1+(5/100)]3
=Rs.18522
C.I=18522-16000
=Rs.2522
Compound Interest:Sometimes it so happens that the borrower and the lender agree to fix up a certain unit of time ,say yearly or half-yearly or quarterly to settle the previous account.
In such cases ,the amount after the first unit of time becomes the principal for the 2nd unit ,the amount after second unit becomes the principal for the 3rd unit and so on.
After a specified period ,the difference between the amount and the money borrowed is called Compound Interest for that period.
Formulae:
Let principal=p,Rate=R% per annum Time=nyears
1.When interest is compounded Annually,
Amount=P[1+(R/100)]n
2.When interest is compounded Halfyearly,
Amount=P[1+((R/2)100)]2n
3.When interest is compounded Quaterly,
Amount=P[1+((R/4)100)]4n
4.When interest is compounded Annually,but time in fractions say 3 2/5 yrs
Amount=P[1+(R/100)]3[1+((2R/5)/100)]
5.When rates are different for different years R1%,R2%,R3% for 1st ,2nd ,
3rd yrs respectively
Amount=P[1+(R1/100)][1+(R2/100)][1+(R3/100)]
6.Present Worth of Rs.X due n years hence is given by
Present Worth=X/[1+(R/100)]n
SIMPLE PROBLEMS
1.Find CI on Rs.6250 at 16% per annum for 2yrs ,compounded annually.
Sol:
Rate R=16,n=2,Principle=Rs.6250
Method1:
Amount=P[1+(R/100)]n
=6250[1+(16/100)]2
=Rs.8410
C.I=Amount-P
=8410-6250
=Rs.2160
Method2:
Iyear------------------6250+1000
\\Interest for 1st yr on 6250
II yr---------------6250+1000+160
\\Interest for I1yr on 1000
C.I.=1000+1000+160
=Rs.2160
2.Find C.I on Rs.16000 at 20% per annum for 9 months compounded quaterly
Sol:
MethodI:
R=20%
12months------------------------20%
=> 3 months------------------------5%
For 9 months,there are '3' 3months
--------16000+800
--------16000+800+40
--------16000+800+40+10+2
=>Rs.2522
MethodII:
Amount=P[1+(R/100)]n
=16000[1+(5/100)]3
=Rs.18522
C.I=18522-16000
=Rs.2522
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