Given the amount invested as 400 with an interest rate of 8%, the number of years it takes to reach 5,500 is calculated as
Thus,
[tex]\begin{gathered} A=5500 \\ P=400 \\ r=8\text{\%}=\frac{8}{100}=0.08 \\ t\text{ is unkown} \end{gathered}[/tex]
Substituting the parameters in the equation, we have
[tex]\begin{gathered} 5500=400(1+0.08)^t \\ \frac{5500}{400}=1.08^t \\ 13.75=1.08^t \end{gathered}[/tex]
Taking the logarithm of both sides to base 10, we have
[tex]\begin{gathered} \log _{10}(13.75)=\log _{10}(1.08)^t \\ 1.1383=t\times0.0334 \\ t=\frac{1.1383}{0.0334}=34.081 \end{gathered}[/tex]
Thus, it will take 34.08 years (nearest hundredth) to reach 5,500.
