Question

Approximately how long will it take to triple an investment at 10% compounded annually​

Answer 1

Answer:

11.526 years

Step-by-step explanation:

Let the investment or Principal be ' P' and it will be tripled in T years

Rate f interest ( R ) = 10 %

Amount = Triple the investment = 3P

We know that

Compound Amount = P[ 1 + R/100 ]^T

where each term indicates :

• P = Principal
• R = Rate of interest
• T = Time period

Substituting the given values

$\Rightarrow \sf 3P = P\bigg[1+\dfrac{10}{100} \bigg]^T \\\\\\ \Rightarrow \sf 3 = \bigg[1+\dfrac{1}{10} \bigg]^T \\\\\\ \Rightarrow \sf 3 = \bigg[\dfrac{11}{10} \bigg]^T$

⇒ 3 = ( 1.1 )^T

As we cannot simplify further, let's take log on both sides

⇒ log 3 = log ( 1.1 )^T

⇒ log 3 = T × log 1.1

⇒ T = log 3 / log 1.1

⇒ T ≈ 11.526

Therefore it takes approximately 11.526 years to triple an investment at 10 % compounded annually.

Answer 2

Answer:

Hey User,

Refer to Attachment.

HOPE IT HELPS YOU.