Question

A sum at r% compound 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

Answer: 8 times

Step-by-step explanation:

A sum becomes double in 3 years

If Principal is 'P'

2P ===== 3 years

4P ===== 6 years

8P ===== 9 years

Hence, it becomes '8' times in 9 years.

ALTERNATE:

A = P[1+ r/100]^n

A == 2P in 3 years

2P = P[1 + r/100]^3         [dividing by 'p' both LHS and RHS]

2 = [1 + r/100]^3 .......(i)            

kP = P[1 + r/100]^9

k = [1 + r/100]^9 ......(ii)

On cubing the eq. (i)

2^3 = { [1 + r/100]^3}^3

8 = [1 + r/100]^9 .....(iii)

COMPARING eq.(ii) & eq.(iii)

k = 8

Hence, 8 times

Answer 2

Answer: The value of k is 8