Mathematics, 19.10.2019 03:30 katherineedwards1105
Tia is investing $2500 that she would like to grow to $6000 in 10 years. at what annual interest rate, compounded quarterly, must tia invest her money? round your answer to two decimal places.
Answers: 3
![\bf 6,000=2,500\left(1+\frac{r}{4}\right)^{4\cdot 10}\implies\cfrac{6000}{2500}=\left(1+\frac{r}{4}\right)^{40} \\ \quad \\ \cfrac{12}{5}=\left(1+\frac{r}{4}\right)^{40}\impliedby \textit{now, taking root }\sqrt[40]{\qquad } \\ \quad \\ \sqrt[40]{\cfrac{12}{5}}=\sqrt[40]{\left(1+\frac{r}{4}\right)^{40}}\implies \sqrt[40]{\cfrac{12}{5}}=1+\cfrac{r}{4} \\ \quad \\ \sqrt[40]{\cfrac{12}{5}}-1=\cfrac{r}{4}\implies 4\left( \sqrt[40]{\cfrac{12}{5}}-1 \right)=r \\ \quad \\ ](/tpl/images/0333/3523/d08f0.png)
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