Question

Can someone please explain how to solve this step by step with answer? Thank you.

Answer 1

a)

well, she put 4000, and she earned in interest 960, so her accumulated amount is just their sum, 4960.

b)

now, it doesn't say, so we're assuming is simple interest, as opposed to compound interest.

$\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&960\\ P=\textit{original amount deposited}\dotfill & \ 4000\\ r=rate\to r\%\to \frac{r}{100}\dotfill\\ t=years\dotfill &3 \end{cases} \\\\\\ 960=(4000)(r)(3)\implies \cfrac{960}{(4000)(3)}=r\implies 0.08=r \\\\\\ \stackrel{\textit{converting to percentage}}{r=0.08\cdot 100}\implies r=\stackrel{\%}{8}$

c)

let's make the rate 1% greater then, and check

$\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill\\ P=\textit{original amount deposited}\dotfill & \ 4000\\ r=rate\to \stackrel{8+1}{9\%}\to \frac{9}{100}\dotfill&0.09\\ t=years\dotfill &3 \end{cases} \\\\\\ I=(4000)(0.09)(3)\implies I=1080 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{at 9\%}}{1080}-\stackrel{\textit{at 8\%}}{960}\implies \stackrel{\textit{that much more}}{120}$