# A sum of money doubles itself in 8 years. What is the rate of interest?

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Hint:- In 8 years money from Interest will be come equal to the principal

amount invested. So, money had been doubled in 8 years.

Let the initial amount of money invested will be Rs. x.

Then after 8 years money had become 2x.

Out of Rs. 2x, money from interest will be 2x – initial amount invested = 2x – x = x.

Let the rate of interest be r.

So, now we will use a simple interest formula.

According to Simple Interest (S.I) formula.

\[ \Rightarrow S.I. = \dfrac{{PRT}}{{100}}\]. Where P is principal amount, R is rate of interest and T will be time period.

So, putting the values in the above formula. We will get,

\[ \Rightarrow x = \dfrac{{xr(8)}}{{100}}\]

On solving the above equation. We will get,

\[ \Rightarrow {\text{ }}r{\text{ }} = {\text{ }}\dfrac{{100}}{8}{\text{ }} = {\text{ }}12.5\]

Hence, the rate of interest to double a money in 8 years will be 12.5% per annum.

Note:- Whenever we came up with this type of problem where we are asked to

find rate of interest then first, we will find the interest on principal amount by

subtracting principal amount from the money after 8 years and then we will

assume rate of interest to be r and then apply, Simple Interest formula and

find the required value of rate of interest.

amount invested. So, money had been doubled in 8 years.

Let the initial amount of money invested will be Rs. x.

Then after 8 years money had become 2x.

Out of Rs. 2x, money from interest will be 2x – initial amount invested = 2x – x = x.

Let the rate of interest be r.

So, now we will use a simple interest formula.

According to Simple Interest (S.I) formula.

\[ \Rightarrow S.I. = \dfrac{{PRT}}{{100}}\]. Where P is principal amount, R is rate of interest and T will be time period.

So, putting the values in the above formula. We will get,

\[ \Rightarrow x = \dfrac{{xr(8)}}{{100}}\]

On solving the above equation. We will get,

\[ \Rightarrow {\text{ }}r{\text{ }} = {\text{ }}\dfrac{{100}}{8}{\text{ }} = {\text{ }}12.5\]

Hence, the rate of interest to double a money in 8 years will be 12.5% per annum.

Note:- Whenever we came up with this type of problem where we are asked to

find rate of interest then first, we will find the interest on principal amount by

subtracting principal amount from the money after 8 years and then we will

assume rate of interest to be r and then apply, Simple Interest formula and

find the required value of rate of interest.

Last updated date: 20th Sep 2023

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