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Question

There is 60% increase in an amount in 6yearsat simple interest. What will be the compound interest ofRs12000after 3years at the same rate?


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Solution

Step 1: Given Information

60% increase in the amount in 6Years at Simple Interest

find CI of Rs12000after 3years at the same rate

We know that,

SI=(PxRxT)100

Where,

SI=SimpleInterestP=PrincipleR=RateofInterestT=Timeperiod

Now,

A=amount

A=SI+P

Step 2: Find the amount

Let RsPbe the Principal

A=P+60%ofP ( As per given)

A=P+60100P

A=100P+60P100 ( On taking LCM )

A=160P100 (Simplify 160P100by dividing by a common factor 20in numerator and denominator separately)

A=8P5--------------- (i)

Step 3: Find the rate of interest R

A=SI+P

8P5=SI+P ( Put the value of Afrom (i) )

8P5=(PxRxT)100+P( Use Formula Of SI)

8P5=(PxRx6)100+P( Put the value of time 6Years)

8P5=P1×R×6100+1 ( Taking Pcommon from both sides)

8P5P=R×6100+1

85-1=R×6100

8-55=R×6100

35×1006=R

10%=R

Or, R=10%----------- (ii)

Step 4: Find Compound Interest

For Compound Interest

A=P1+R100nwhere n=timeperiod

A=120001+101003 {putting the value of R from equation (ii)}

A=120001+1103

A=1200011103

A=1200011×11×1110×10×10

A=12×1331

A=15,972

CompoundInterest(CI)=Amount(A)Principal(P)

CI=1597212000

CI=3972

Hence, CI=3972 for 3yearsat the same rate.


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