A sum of money at compound interest doubles itself in 4 years. In how many years does the sum become 8 times of itself at the same rate of interest?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e 12
A = P × [1 + (r/100)]T [Where A = Amount, P = Principal, r = rate of interest, T = time period]
According to the question -
A = 2 × Principal, T = 4 years
⇒ A = P × [1 + (r/100)]T
⇒ 2P = P × [1 + (r/100)]4
⇒ 2 = [1 + (r/100)]4 ...(1
If sum becomes 8 times in T years -
Then, A = 8P
⇒ 8P = P × [1 + (r/100)]T
⇒ 8 = [1 + (r/100)]T
⇒ 23 = [1 + (r/100)]T ...(2
From equation (1 and (2, we get -
⇒ {[1 + (r/100)]4}3 = [1 + (r/100)]T
⇒ [1 + (r/100)]12 = [1 + (r/100)]T
⇒ T = 12 years