Question

You invest 1,000 in an account that pays an interest rate of 12%How many years would it take for your account to reach 3,105.85?

Answer 1

10 years

Step-by-step explanation:

We will use the given equation:

`A=P(1+r)^t`

Where P is the amount invested, so it is 1,000

r is the interest rate percentage which is equal to 12% or 0.12

t is the time in years

A is the amount in your account after t years, so it is 3,105.85

Replacing the values, we get

`\begin{gathered} 3105.85=1000(1+0.12)^t \\ 3105.85=1000(1.12)^t_{} \end{gathered}`

Now, we can solve the equation for t. Divide both sides by 1000

`\begin{gathered} (3105.85)/(1000)=(1000(1.12)^t)/(1000) \\ 3.10585=1.12^t \end{gathered}`

Apply logarithm to both sides

`\begin{gathered} \ln (3.10585)=\ln 1.12^t \\ \ln (3.10585)=t\ln (1.12) \\ 1.1333=t\cdot(0.1133) \end{gathered}`

Divide both sides by 0.1133

`\begin{gathered} (1.1333)/(0.1133)=(t\cdot(0.1133))/(0.1133) \\ 10=t \end{gathered}`

Therefore, it would take 10 years for your account to reach $3,105.85