### Interests

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## SI & CI

Simple Interest Definition

If the interest on a sum borrowed for certain period is calculated uniformly, it is called SI & CI(SI).

SI & CI , SI =
100
P * R * T

where , P = Principal { It is the sum of money borrowed or lent out for a certain period. }
R = rate of interest.
T = time period.

Important formulae :

1. If a sum of money becomes n times in T years at SI & CI, then the rate of interest per annum can be given be

R =
T
100 ( n - 1 )
%

2. If an amount P1 is lent out at SI & CI of R1% per annum and another amount P2 at SI & CI rate of R2% per annum, then the rate of interest for the whole sum can be given by

R =
P1 + P2
P1R1 + P2R2

3. If a certain sum of money is lent out in n parts in such a manner that equal sum of money is obtained at SI & CI on each part where interest rates are R1, R2, ... , Rn respectively and time periods are T1, T2, ... , Tn respectively, then the ratio in which the sum will be divided in n parts can be given by

R1T1
1
:
R2T2
1
: .....
R3T3
1

4. If a certain sum of money P lent out for a certain time T amounts to P1 at R1% per annum and to P2 at R2% per annum, then

P =
R1 - R2
P2R1 - P1R2

T =
P2R1 - P1R2
P1 - P2
* 100 years

Compound Interest Definition

In compound interest method, interest for each period is added to the principal before interest is calculated for the next period. In other words, the principal grows as the interest gets added to it.
Importanat Formulae

1. Let Principal = P, Rate = R% per annum, Time = T years and A = Amount due after T years. Then

* Case 1: When interest is compounded annually

A = P * ( 1 +
100
R
)T

* Case 2: When interest is compounded half-yearly

A = P * ( 1 +
100
(R/2)
)2T

* Case 3: When interest is compounded quarterly

A = P * ( 1 +
100
(R/4)
)4T

* Case 4: When interest is compounded annually, but time is in fraction, say 4 * 1/3 years

A = P * ( 1 +
100
R
)4 * ( 1 +
100
1/3 * R
)

* Case 5: When rates are different for different years, say R1%, R2% and R3% for 1st, 2nd and 3rd year respectively.

A = P * ( 1 +
100
R1
) ( 1 +
100
R2
) ( 1 +
100
R3
)

2. Wherever the term compound interest is used without specifying the period in which the interest is compounded, it is assumed that interest is compounded annually.

3. Compound Interest (CI) = A - P

4. Simple Interest and Compound Interest for 1 year at a given rate of interest per annum will be equal.