a certain sum becomes 16 times in 4 year at compound interest compounded annually .what is the rate of interest.
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Answer:
Step-by-step explanation:
Let the required rate of interest be R.
Consider, the principal be P for time n years.
After 4 years, the amount is 16 times the principal. Here,
n = 4 years
Amount = 16 P
We know that,
\rm Amount = P \left( 1 + \dfrac{R}{100}\right)^nAmount=P(1+100R)n
\implies \rm 16P = P \left(\dfrac{100 + R}{100}\right)^4⟹16P=P(100100+R)4
\implies \rm (2)^4 = \left(\dfrac{100 + R}{100}\right)^4⟹(2)4=(100100+R)4
On cancelling power 4 both sides,
\implies \rm 2 = \dfrac{100 + R}{100}⟹2=100100+R
On cross-multiplying both sides -
\rm \implies 100 + R = 200⟹100+R=200
\implies \rm R = 200 - 100⟹R=200−100
\boxed{\bf \therefore \: R = 100 \%}∴R=100%
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