Question

4. An initial investment of S4 is worth $100 after 5 years. If the annual growth reflects a geometric sequence, approximately how much will the investment be worth after 11 years?•220•5590•244•12500

Answer 1

The formula for geometric sequence is,

`\begin{gathered} U_n=ar^(n-1) \\ \end{gathered}`

Where,

`\begin{gathered} U_5=\text{ \$100} \\ n=5\text{years} \\ a=\text{ \$4} \end{gathered}`

Substituting the values into the formula above,

`\begin{gathered} U_5=ar^(5-1)=ar^4 \\ 4r^4=100 \\ r^4=(100)/(4) \\ r^4=25 \\ \sqrt[4]{r^4}=\sqrt[4]{25} \\ r=\sqrt[4]{25} \end{gathered}`

After 11 years,

`\begin{gathered} U_(11)=ar^(11-1)=ar^(10) \\ U_(11)=ar^(10) \\ U_(11)=4(\sqrt[4]{25})^(10) \\ U_(11)=4*3125=12500 \end{gathered}`

Hence, the amount after 11 years is $12,500