Question

How long will it take for an investment to triple if it is compounded continuously at 12%

Answer 1

Answer:

9.694 years

Step-by-step explanation:

Let the investment is $P.

So, we are asked to determine the time it will grow to triple with the compound interest rate of 12%.

Let the time is y years.

So, from the formula of compound interest we can write

$3P = P(1 + \frac{12}{100} )^{y}$

⇒ $(1 + \frac{12}{100} )^{y} = 3$

⇒ $(1.12)^{y} = 3$

Now, taking log both sides we get,

y log 1.12 = log 3 {Since, $\log a^{b} = b \log a$ }

⇒ 0.04922y = 0.477712

⇒ y = 9.694 years (Answer)