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,
![\begin{gathered} A=5500 \\ P=400 \\ r=8\text{\%}=(8)/(100)=0.08 \\ t\text{ is unkown} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/x8akr97nhr87420ppr7sbumph32ejuk891.png)
Substituting the parameters in the equation, we have
![\begin{gathered} 5500=400(1+0.08)^t \\ (5500)/(400)=1.08^t \\ 13.75=1.08^t \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/24ulq96tz2amehbvyu4oa7pizv0fj5l6ll.png)
Taking the logarithm of both sides to base 10, we have
![\begin{gathered} \log _(10)(13.75)=\log _(10)(1.08)^t \\ 1.1383=t*0.0334 \\ t=(1.1383)/(0.0334)=34.081 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/9wa3gd3zh95p23i5h9c4mosmxbyvwkadm6.png)
Thus, it will take 34.08 years (nearest hundredth) to reach 5,500.