Question

A sum of money doubles itself in 5 years. How much time will it take for it to quadruple at the same rate of interest? please give me solution ​

Answer 1

Given,

• Sum of money doubles itself in 5 years.

• Interest is same as principal amount.

Here,

• Interest (I) = 1

• Principal amount (P) = 1

• Time period (t) = 5 years

We know the equation:

$\boxed{\sf{I=\dfrac{P\times r\times t}{100}}}$

$\sf{\implies 1=\dfrac{1\times r\times 5}{100}}$

$\sf{\implies 1=\dfrac{5r}{100}}$

$\sf{\implies 5r=100}$

$\sf{\implies r=\dfrac{100}{5}}$

$\sf{\implies r=20 \ \%}$

$\boxed{\sf{\therefore \ Rate \ of \ interest=20 \ \%}}$

Now we have to find how much time will it take for it to quadruple at the same rate of interest.

Here,

• Principal amount = p

• Interest = 3p

$\sf{\implies 3p=\dfrac{p\times 20\times T}{100}}$

$\sf{\implies 3=\dfrac{20\times T}{100}}$

$\sf{\implies 3=\dfrac{T}{5}}$

$\sf{\implies T=5\times 3}$

$\sf{\implies T=15 \ years}$

$\boxed{\sf{\therefore \ Time \ taken=15 \ years}}$