Question

A sum of Rs. 8000 invested at compound interest doubles in five years.
After twenty years it becomes:

Answer 1

compound interest double in 5 yrs

after 20 years = 5 + 5 + 5 + 5

= double +double+double+double

it becomes 8times.

Answer 2

Answer:

The resultant amount after 20 years = 128000  or 16 times of the initial amount

Step-by-step explanation:

Given data  

A sum of Rs. 8000 is invested at compound interest  

the money is doubled in 5 years

Here we need to find the resultant amount after 20 years  

from given data principal amount P = 8000, time period t = 5 years

let R be the rate of interest

the resultant amount after 5 years =  $P [ 1+ \frac{R}{100} ]^{t}$  

                                                         = $8000[1 + \frac{R}{100} ]^{5}$

given that the resultant amount is doubled after 5 years

                      $8000[ 1 + \frac{R }{100} ]^{5} = 16000$

                       $[1 + \frac{R}{100} ]^{5} = \frac{16000}{8000}$  

                       $[ 1 + \frac{R}{100} ]^{5} = 2$ _ (1)

now calculate the resultant amount after 20 years

                     $= 8000[ 1 + \frac{R}{100}]^{20}$

                     =  $8000 [( 1+ \frac{R}{100})^{5} ]^{4}$

                     =  8000 (2⁴)            [ from (1) ]

                     =  8000 (16)             [ 2⁴ = 16]

                     =  128000

the resultant amount after 20 years = 128000  or 16 times of the initial amount