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# 4 Fast Tricks to Solve Compound Interest

In the context of compound interset, sometimes there arises a situation when the borrower and the lender fix up a certain unit of time (like yearly or half-yearly or multiples of n where n is the no of years infractions)
In such case, the amount becomes the principle for the second unit of time after the first unit of time(n=1) ## Different cases are as follows:-

### Case I

when the compound interest is calculated half-yearly
if the rate is r% per annum and time is n years then the corresponding rate and time are n/2 and 2*n respectively.
A = P[1 + (r²)/100]²n
where A= amount
P=principle
r=rate
t=time in years

#### Illustration

P= Rs 15000
r=10%
t=1 Year
compounded half yearly
then according to above formula
r=10/2 = 5%
t=2 x 1=2 half year
A = 15000 x [(1 + 5/100)²] = Rs 16537.50

### Case 2

when comound interst is calculated quarterly
in this case rate = r/4% and time 4 x n quarter years
A= P[1+(r/4)/100]⁴ x n

#### llustratin

P = Rs 15625
t = 9 months = 3 quarters
r= 16/4 = 4%
A= 15625 x (1+4/100)³ = Rs 1951

#### Important note :

The difference between the compound interest and simple interst over a period of two year is given by
[C.I - S.I = P(r/100)²]
where symbols have their usual meanings.

### Case 3

When interset is compounded annualy but time is in fraction says years
Amount = P(1 + r/100)³ x (1+ (2/5r)/100)

#### Illustration

calculate difference between compound interest on Rs 5000 for 4 % per annum compounded yearly and half yearly
C.I(yearly) = 5000 x (1+4/100) x (1+0.5 x 4/100)
= Rs 5304
C.I(half yearly) = 5000 x (1+2/100)³
= Rs 5306.04
Difference = 5306.04-5304 = RS 2.04

### Case 4

Amount Due in n years for a sum of Rs.x
A = x/(1 + r/100)ⁿ

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