Question

find the rate at which a sum of money will double itself in 3 years if the interest is compounded annually

Answer 1

Let the sum be Rs x
After 3 years the sum will double itself.
Therefore amount = Rs 2x
Let rate of interest = r %

Amount =  P (1+r/100)^n
2x = x (1+ r/100)³
2x/x = [(100+ r) /100]³
(2)^1/3 = (100+r)/100
1.26 = (100+r)/100        (2^1/3 = 1.2599) [taking 2^1/3 = 1.26]
126 = 100+r
r = 26%

Answer 2

Let Principal be p.

Given that Sum of money will double itself.

Given Time n = 3 years.

Given Amount = 2P.

We know that A = P(1 + r/100)^n

                        2P = P(1 + r/100)^3

                       2 = (1 + r/100)^3

                       $(1 + \frac{r}{100} ) = \sqrt[3]{2}$

                      1 + r/100 = 1.259

                      r/100 = 1.259 - 1

                      r/100 = 0.259

                      r = 100 * 0.259

                      r = 25.9.


Therefore the rate of interest is 25.9% (or) 26% per annum.


Hope this helps!