Find the interest rate needed for an investment of $10,000 to grow to an amount of $11,000 in 4 years if interest is compounded quarterly. (Round your answer to the nearest hundredth of a percent.) %

Answer:[tex]2.39\%[/tex]  Step-by-step explanation:we know that    The compound interest formula is equal to  [tex]A=P(1+\frac{r}{n})^{nt}[/tex]  where  A is the Final Investment Value  P is the Principal amount of money to be invested  r is the rate of interest  in decimal t is Number of Time Periods  n is the number of times interest is compounded per year in this problem we have  [tex]t=4\ years\\ P=\$10,000\\A=\$11,000\\ r=?\\n=4[/tex]  substitute in the formula above  [tex]11,000=10,000(1+\frac{r}{4})^{4*4}[/tex]  [tex]1.1=(1+\frac{r}{4})^{16}[/tex]  Elevated both sides to (1/16)[tex]1.005975=(1+\frac{r}{4})[/tex]  [tex]0.005975=\frac{r}{4}[/tex]  [tex]r=0.005975*4=0.0239[/tex]  Convert to percent[tex]0.0239*100=2.39\%[/tex]