If a certain sum becomes three times in 4 years at compound interest, then in how many years, will it become 9 times?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 8
At compound interest the sum is multiplied by the same factor in every equal period, \((1+r)^n\) after \(n\) years. If it becomes 3 times in 4 years, the next 4 years multiply it by 3 again.
\(P(1+r)^4=3P\), so \((1+r)^4=3\)
\(9P=3^2P=\left[(1+r)^4\right]^2P=(1+r)^8P\)
So the sum becomes 9 times in 8 years
Tip: A sum that becomes \(n\) times in \(t\) years at compound interest becomes \(n^k\) times in \(kt\) years (3 times in 4 years, 9 times in 8, 27 times in 12). At simple interest it would not: 3 times in 4 years means interest of 2P in 4 years, so 9 times needs 8P of interest, which takes 16 years.