Answer:
10 years
Explanation:
We will use the given equation:
[tex]A=P(1+r)^t[/tex]
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
[tex]\begin{gathered} 3105.85=1000(1+0.12)^t \\ 3105.85=1000(1.12)^t_{} \end{gathered}[/tex]
Now, we can solve the equation for t. Divide both sides by 1000
[tex]\begin{gathered} \frac{3105.85}{1000}=\frac{1000(1.12)^t}{1000} \\ 3.10585=1.12^t \end{gathered}[/tex]
Apply logarithm to both sides
[tex]\begin{gathered} \ln (3.10585)=\ln 1.12^t \\ \ln (3.10585)=t\ln (1.12) \\ 1.1333=t\cdot(0.1133) \end{gathered}[/tex]
Divide both sides by 0.1133
[tex]\begin{gathered} \frac{1.1333}{0.1133}=\frac{t\cdot(0.1133)}{0.1133} \\ 10=t \end{gathered}[/tex]
Therefore, it would take 10 years for your account to reach $3,105.85
