Question

Yehudy invested $19,250 in a simple interest account. After 6 years and no additional deposits or withdrawals, the account balance was $22,957.55. Find the interest rate for the account. Round to the nearest hundredth of a percent if needed.

Answer 1

answer: 3.21%


step by step explanation:
interest = (1/t)(A/P - 1)

Answer 2

$~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &\ 22957.55\\ P=\textit{original amount deposited}\dotfill & \ 19250\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &6 \end{cases} \\\\\\ 22957.55=19250[1+(\frac{r}{100})(6)]\implies 22957.55=19250\left( 1 + \cfrac{3r}{50} \right)$

$\cfrac{22957.55}{19250}=1 + \cfrac{3r}{50}\implies \cfrac{22957.55}{19250}-1=\cfrac{3r}{50} \\\\\\ \cfrac{50}{3}\left( \cfrac{22957.55}{19250}-1 \right)=r\implies \stackrel{\%}{3.21}=r$