The simple interest on a sum of money is \( \frac{4}{9} \) of the principal. If rate percent and time…

$\text{S.I.}=\frac{PRT}{100}=\frac49P$ with $R=T$, so $\frac{R^2}{100}=\frac49$. Then $R^2=\frac{400}{9}$ and $R=\frac{20}{3}=6\tfrac23\%$, with the time also $6\tfrac23$ years. Check: $\frac{20}{3}\times\frac{20}{3}\div100=\frac{400}{900}=\frac49$. A rate of $8\tfrac23\%$ would make the interest $\frac{676}{900}$ of the principal, far more than $\frac49=\frac{400}{900}$.