Question
The difference between compound interest and simple interest on an amount of ₹15,000 for 2 years is ₹96. What is the rate of interest per annum?
Answer: Option C
:
C
Given that, principal, P=₹15000and time period, n=2 years .
Let the rate of interest per annum be r.
Simple interest in 2 years
S.I=15000×r×2100
⇒S.I=300r
Compound interest C.I=A−P=15000(1+r100)2−15000, here, A is the amount.
Given that C.I−S.I=96
(Since C.I > S.I)
⇒15000(1+r100)2−15000−300r=96
⇒15000(1+r100)2−300r=15096
⇒15000(1+r210000+2r100)−300r=15096
⇒15000+15r210+300r−300r=15096
⇒15r210=96
⇒15r2=960
⇒r2=64
⇒r=±8
∵ Rate of interest cannot be negative, so r=8%
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:
C
Given that, principal, P=₹15000and time period, n=2 years .
Let the rate of interest per annum be r.
Simple interest in 2 years
S.I=15000×r×2100
⇒S.I=300r
Compound interest C.I=A−P=15000(1+r100)2−15000, here, A is the amount.
Given that C.I−S.I=96
(Since C.I > S.I)
⇒15000(1+r100)2−15000−300r=96
⇒15000(1+r100)2−300r=15096
⇒15000(1+r210000+2r100)−300r=15096
⇒15000+15r210+300r−300r=15096
⇒15r210=96
⇒15r2=960
⇒r2=64
⇒r=±8
∵ Rate of interest cannot be negative, so r=8%
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