Question

My final balance after 48 months was $896.00 if I originally put $800.00 into the bank what was the interest rate

Answer 1

assuming is simple interest rate, as opposed to compound interest.

bearing in mind that 48 months is really 2 years.

$\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&896\\ P=\textit{original amount deposited}\dotfill & \ 800\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &2 \end{cases}$

$\bf 896=800[1+r(2)]\implies \cfrac{896}{800}=1+2r\implies \cfrac{28}{25}=1+2r \\\\\\ \cfrac{28}{25}-1=2r\implies \cfrac{3}{25}=2r\implies \cfrac{3}{50}=r\implies 0.06=r \\\\\\ \stackrel{\textit{converting to percentage}}{0.06\cdot 100=r}\implies \stackrel{\%}{6}=r$