Answer:
26 years
Explanation:
The amount at the end of t years can be calculated as:
[tex]A=P(1+r)^t[/tex]Where P is the principal and r is the interest rate.
If we want to find the doubling time, we need to replace A by 2P and solve for t, so we get:
[tex]\begin{gathered} 2P=P(1+0.027)^t \\ \frac{2P}{P}=\frac{P(1+0.027)^t}{P} \\ 2=(1+0.027)^t \end{gathered}[/tex][tex]\begin{gathered} 2=1.027^t \\ \log 2=t\log 1.027 \\ \frac{\log 2}{\log 1.027}=t \\ 26.01=t \end{gathered}[/tex]Therefore, the doubling time for this situation is approximately 26 years.
