Question

A sum of money earning compound interest annually doubles itself after 4 years. What is the rate of interest ? (take 2^1/4 = 1.19)

1. 14%
2. 19%
3. 18%
4. 15%

Answer 1

Correct Answer - Option 2 : 19%

Given data:

Time period t = 4 years 

After the four years  Amount = 2p

Formulae used :

Amount = p (1 + r/100 )^t

Calculations:

Let the principal be 'p'

Rate percent be 'r'

2p = p (1 + r/100)⁴

⇒ 2 = (1 + r/100)⁴

⇒ 2^1/4 = 1 + r/100

⇒ 2^1/4 = (100 + r)/100

⇒ 1.19 × 100  = 100 + r

⇒ 119 = 100 + r

⇒ r = 119 - 100

⇒ r = 19 %

∴ The rate of interest is 19%