Question

A sum of money invested at a certain rate doubles itself in 10 years. How much time will it take to triple itself at the same rate?

Answer 1

It will take 15 years for the sum of money to triple itself.

Step-by-step explanation:

Let P be the initial principal amount. Since the sum doubles itself in 10 years, after 10 years, the amount will be 2P.

To triple itself, the amount needs to reach 3P. We can set up the following equation:

2P * (1 + r)^t = 3P

where r is the annual interest rate and t is the number of years.

Dividing both sides by 2P, we get:

(1 + r)^t = 1.5

Taking the natural logarithm of both sides, we get:

ln(1.5) = t * ln(1 + r)

Solving for t, we get:

t = ln(1.5) / ln(1 + r)

Since the sum doubles itself in 10 years, we know that (1 + r)^10 = 2. Plugging this into the equation above, we get:

t = ln(1.5) / ln(2^(1/10))

t = ln(1.5) / (1/10 * ln(2))

t = 15 years

Therefore, it will take 15 years for the sum of money to triple itself.