Question

Amanda deposits $500 into a savings account
arning simple interest at an annual rate of 8%. tori deposits $1,000 into a
vings account earning simple interest at an annual rate of 2.5%. neithe
i makes any additional deposits or withdrawals. which girl's account
i reach a balance of $1,500 first? justify your answer.

Answer 1

$~~~~~~ \stackrel{\textit{\LARGE Amanda}}{\textit{Simple Interest Earned Amount}} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \ 1500\\ P=\textit{original amount deposited}\dotfill & \ 500\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases} \\\\\\ 1500=500[1+(0.08)(t)]\implies \cfrac{1500}{500}=1+0.08t\implies 3= 1 + 0.08t \\\\\\ 2 = 0.08t\implies \cfrac{2}{0.08}=t\implies \boxed{25=t} \\\\[-0.35em] ~\dotfill$

$~~~~~~ \stackrel{\textit{\LARGE Tori}}{\textit{Simple Interest Earned Amount}} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \ 1500\\ P=\textit{original amount deposited}\dotfill & \ 1000\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years \end{cases}$

$1500=1000[1+(0.025)(t)]\implies \cfrac{1500}{1000}=1+0.025t\implies \cfrac{3}{2}=1 + 0.025t \\\\\\ \cfrac{3}{2}-1= 0.025t\implies \cfrac{1}{2}=0.025t\implies \cfrac{ ~~ \frac{1}{2} ~~ }{0.025}=t\implies \boxed{20=t}$

well, clearly Tori is Da Bomb!.