The correct answer is option (B):
10 years
Here's how to solve this compound interest problem:
Let P be the principal amount.
The problem states the sum triples in 5 years. Let the rate of interest be r. We can represent this with the compound interest formula:
3P = P (1 + r)^5 (Where 3P is the amount after 5 years, P is the principal, and (1+r) is the growth factor raised to the power of the number of years.)
Dividing both sides by P, we get:
3 = (1 + r)^5
Now, we want to know how long it takes for the amount to become nine times the principal (9P). Let 't' be the number of years.
9P = P (1 + r)^t
Dividing both sides by P:
9 = (1 + r)^t
Notice that 9 is the square of 3 (9 = 3^2). We can substitute the value we found earlier:
9 = [(1 + r)^5]^2
9 = (1 + r)^(5*2)
9 = (1 + r)^10
Therefore, t = 10 years.
The amount will become nine times the principal in 10 years. This is because the process of tripling happens repeatedly. Since the initial amount tripled in 5 years, and we want it to be nine times the initial amount (which is tripling twice: 3 * 3 = 9), we know it will take two lots of 5 years.