A certain sum of money invested at some rate of simple interest triple

• Interests

A certain sum of money invested at some rate of simple interest triple itself in 4 years. In how many years the principal will become 9 times of itself at the same rate?

Solution

When the principal is in simple interest, the interest for every year will be same. In 4 years the amount becomes 3 times the principal.

A = P + I

3P = P + I

⇒ I = 2P

The interest is 2 times the principal in 4 years or equal to principal in 2 years. The interest will be equal to P in 2 years.

So interest will be 8P in 16 years. 

Amount after 16 years = P + 8P = 9P

Hence, the answer is 16 years.