Question

9. A certain sum of money invested at a certain rate of compound interest doubles in 5 years. In how many years will it become 4 times?​

Answer 1

${ \underline{ \underline {\bf Question}}}$

A certain sum of money invested at a certain rate of compound interest doubles in 5 years. In how many years will it become 4 times ?

$\large\tt{Answer}$

$\tt10 \: years$

$\huge\tt{Solution}$

Let the certain sum of money be ₹ P

So , Amount will be ₹ 2P

We know that

$\boxed{ \rm A = P( 1 + \dfrac{R}{100})^n}$

On Substituting the values we get,

$: \implies \rm 2 \cancel{P}= \cancel{P}( 1 + \dfrac{R}{100})^5 \\ : \implies \sf2 = ( 1 + \dfrac{R}{100})^5 \longrightarrow(1) \star$

Now , we have to calculate the total time ( in years ) when this amount will become 4 times .

$: \implies \rm 4\cancel{P}= \cancel{P}( 1 + \dfrac{R}{100})^n \\ \sf(2) ^{2} = ( 1 + \dfrac{R}{100})^n$

Substitute the eq (1) in place of 2 .

$\rightarrow [\rm(1 + \dfrac{R}{100}) ^{5}] ^{2} = ( 1 + \dfrac{R}{100})^n$

$: \implies \sf(1 + \dfrac{R}{100}) ^{10} = ( 1 + \dfrac{R}{100})^n$

$: \implies \sf( \cancel{1 + \dfrac{R}{100}}) ^{10} = ( \cancel{ 1 + \dfrac{R}{100}})^n$

On Comparing ,

$\colorbox{red}{n = 10}$

Conclusion

This means that after an interval of 10 years the sum will. become 4 times of original amount.

Thankyou

Answer 2

Answer:

The principal will become 4 times in 10 years.

Step-by-step explanation:

• Compound interest: Compound interest is the interest which is calculated over the sum of principal and last year's interest.
• Compound interest = Amount - pricipal

                                         = $P(1+\frac{r}{100} )^n$ - P

       Amount =  $P(1+\frac{r}{100} )^n$

     Where, P = principal,   r = rate of interest   and n = time

• According to the question, 'P' becomes '2P' in 5 years.

            So, 2P = $P(1+\frac{r}{100} )^5$

                   $(1+\frac{r}{100} )^5$ = 2................(1)

• Suppose P becomes 4P in 't' years, 4P = $P(1+\frac{r}{100} )^t$

                                                                                $(1+\frac{r}{100} )^t$ = 4.......(2)

      Taking square on both sides of equation (1), $(1+\frac{r}{100} )^{5\times2}$= 2²

                                                                                $(1+\frac{r}{100} )^{10}$ = 4.......(3)

     Comparing (2) and (3),  $(1+\frac{r}{100} )^t$ =  $(1+\frac{r}{100} )^{10}$

                                              t = 10

    ∴ The principal will become 4 times in 10 years.

To know more about compound interest visit the link given below:

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