Question

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 1

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%