business mathematics

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.

Formula:

Let principal=p, Rate=R% per annum, Time=n years

1.When interest is compounded Annually,
Amount=P[1+(R/100)]n
2.When interest is compounded Half yearly,
Amount=P[1+((R/2)100)]2n
3.When interest is compounded Quarterly,
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

Principal or Sum:-
The money borrowed or lent out for a certain period is called Principal or the Sum.

Interest:-
Extra money paid for using others money is called Interest.

Simple Interest:-
If the interest on a sum borrowed for a certain period is reckoned uniformly,then it is called Simple Interest.



Formula:
Principal = P
Rate = R% per annum
Time = T years. Then,

(i)Simple Interest(S.I)= (P*T*R)/100

(ii) Principal(P) = (100*S.I)/(R*T)
Rate(R) = (100*S.I)/(P*T)
Time(T) = (100*S.I)/(P*R)

Introduction:

In any type of problems,a set of numbers is given in such a way
that each one except one satisfies a particular definite
property.The one which does not satisfy that characteristic is
to be taken out. Some important properties of numbers are
given below :

1.Prime Number Series
Example:
2,3,5,7,11,..............
2.Even Number Series
Example:
2,4,6,8,10,12,...........
3.Odd Number Series:
Example:
1,3,5,7,9,11,...........
4.Perfect Squares:
Example:
1,4,9,16,25,............
5.Perfect Cubes:
Example:
1,8,27,64,125,.................
6.Multiples of Number Series:
Example:
3,6,9,12,15,..............are multiples of 3
7.Numbers in Arthimetic Progression(A.P):
Example:
13,11,9,7................
8.Numbers in G.P:
Example:
48,12,3,.....
Some More Properties:

1. If any series starts with 0,3,.....,generally the relation
will be (n2-1).
2. If any series starts with 0,2,.....,generally the relation
will be (n2-n).
3. If any series starts with 0,6,.....,generally the relation
will be (n3-n).
4. If 36 is found in the series then the series will be in n2
relation.
5. If 35 is found in the series then the series will be in
n2-1 relation.
6. If 37 is found in the series then the series will be in n2+1
relation.
7. If 125 is found in the series then the series will be in n3
relation.
8. If 124 is found in the series then the series will be in n3-1
relation.
9. If 126 is found in the series then the series will be in n3+1
relation.
10. If 20,30 found in the series then the series will be in n2-n
relation.
11. If 60,120,210,........... is found as series then the series
will be in n3-n relation.
12. If 222,............ is found then relation is n3+n
13. If 21,31,.......... is series then the relation is n2-n+1.
14. If 19,29,.......... is series then the relation is n2-n-1.
15. If series starts with 0,3,............ the series will be on
n2-1 relation.