At what rate a sum doubles itself in 8 year 4 months. (2024)

Given: A sum doubles itself in 8 year 4 months.

To find: Here we have to find the rate of interest at which a sum doubles itself in 8 year 4 months.

Solution:

Let the actual amount be = $a$

Now, this sum is doubled in 8 year 4 months:

Amount after 8 years 4 months = $2a$

Simple interest paid in 8 years 4 months:

SI = Amount after 8 years 4 months $-$ Actual amount

SI = $2a\ -\ a\ =\ a$

8 years 4 months = $\frac{25}{3}$ years

Also,

$SI\ =\ \frac{P\ \times \ R\ \times \ T}{100}$

$a\ =\ \frac{a\ \times \ R\ \times \ 25}{100\ \times\ 3}$

$a\ =\ \frac{a\ \times \ R}{4\ \times\ 3}$

$a\ =\ \frac{a\ \times \ R}{12}$

$\frac{12a}{a} =\ R$

$\mathbf{R\ =\ 12\%}$

So, rate of interest at which a sum doubles itself in 8 year 4 months is 12%.