Question

find the rate at which a sum of money will double itself in 2 years if the interest is compounded annually.

Answer 1

Let the sum = p

time = 2 years

It doubles itself. So amount = 2p

Let the rate = r

$a = p{(1 + \frac{r}{100} )}^{t} \\ \\ 2p = p{(1 + \frac{r}{100} )}^{2}$

$2 = {(1 + \frac{r}{100}) }^{2} \\ \\ 1 + \frac{r}{100} = \sqrt{2} = 1.414$

$\frac{r}{100} = 1.414 - 1 = 0.414 \\ \\ r = 0.414 \times 100 = 41.4$

Hence, rate of interest is 41.4%

Answer 2

Hi
Nice question

Solution:-

Let the sum of money be p.

After doubling itself, it becomes 2p.

So amount = 2p

Time rate = 2 years

Let the rate be r.

Using the formula :-
$a = p {(1 + \frac{r}{100} )}^{t} \\ \\ 2p = p {(1 + \frac{r}{100} )}^{2} \\ \\ 2 = {(1 + \frac{r}{100}) }^{2} \\ \\ 1 + \frac{r}{100} = \sqrt{2} \\ \\ 1 + \frac{r}{100} = 1.414 \\ \\ \frac{r}{100} = 1.414 - 1 \\ \\ \frac{r}{100} = 0.414 \\ \\ r = 41.4$

Hope this helps you.