Question

a sum of amount at certain rate of compund interest doubles in 3 years.in 9 years it will be k times of the original principal.what is the value of k?

Answer 1

The accumulated amount formula :

P(1 + i) ⁿ

P = principal amount

i = interest rate

n = Time in years

Let P be the principle amount then:

The amount in three years is :

2p = p(1 + i) ³

(1 + i) ³ = 2

1 + i = ∛2

1 + i = 1.25992

i = 1.25992 - 1

i = 0.25992

= 25.992%

The amount in 9 years

P(1 + i) ⁹ = kp

(1 + 0.25992)⁸ = k

(1.25992)⁸ = 6.345 times

k = 6.345 times

Answer 2

as per Question

Amount Double in 3 years

so let X is initial amount after 3 years = 2X

after next 3 years = 4X (i.e. after 6 years)

After Next 3 years = 8X ( i.e. 9 years)

so after 9 years amount will be 8 times of Initial Amount