Question

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

Answer 1

9.694 years

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 + (12)/(100) )^(y)`

⇒
`(1 + (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)