Question

Mark invests Php 5,000. Approximately how long will it take for the investment to double if the rate is 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

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

⇒ 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

Step-by-step explanation:

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

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

⇒ 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.