Question

sum.of money at simple interest doubles itself in 20 years then find the rate of interest​

Answer 1

AnswEr :

• At 5% rate of interest, sum of money doubles itself in 20 years.

GivEn :

• Total Time = 20 years

To find :

• Rate of interest (R) = ?

Formula usEd :

You can find the rate of interest using the following formula,

$\dag \large \: { \boxed{ \rm{A=P \bigg( 1 + \dfrac{TR}{100} \bigg) }}}$

Where,

• A = amount

• P = Principal

• R = rate of interest

• T = time period

SoluTion :

Let us assume that the principle be x.

Then,

As it is given that, sum of the money given gets doubled within 20 years, So,

• Amount (A) = 2x

We know that,

$: \implies \sf \: \: \: A=P \bigg( 1 + \dfrac{TR}{100} \bigg)$

$: \implies \sf \: \: \: 2x= x \bigg( 1+ \dfrac{20 R}{100} \bigg)$

$:\implies\sf \: \: \: \dfrac{2x}{x} = 1+ \dfrac{20 R}{100}$

$: \implies \sf \: \: \: 2-1 = \dfrac{R}{5}$

$: \implies \sf \: \: \: R =5 \times 1$

$:\implies \sf \: \: \: { \underline{ \boxed{ \sf{ \purple{R =5 \: \%}}}}} \: \bigstar$

Therefore, at 5% rate of interest, sum of the money doubles itself in 20 years.

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