for a Principal of $2000 to double up, it will be $4000, so with a rate of 8%, when is that?
[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount}
\\\\
A=P(1+rt)\qquad
\begin{cases}
A=\textit{accumulated amount}\to &\$4000\\
P=\textit{original amount deposited}\to& \$2000\\
r=rate\to 8\%\to \frac{8}{100}\to &0.08\\
t=years
\end{cases}
\\\\\\
4000=2000(1+0.08t)\implies \cfrac{4000}{2000}=1+0.08t\implies 2=1+0.08t
\\\\\\
1=0.08t\implies \cfrac{1}{0.08}=t\implies 12.5=t[/tex]
$12000 at 8% rate for 7years with simple interest?
[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount}
\\\\
A=P(1+rt)\qquad
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to& \$12000\\
r=rate\to 8\%\to \frac{8}{100}\to &0.08\\
t=years\to &7
\end{cases}
\\\\\\
A=12000(1+0.08\cdot 7)\implies A=18720[/tex]
now, for these ones, we'll assume the interest is still 8%, simple interest, and is asking for the Principal, how much would you put in in order to get $5000 for 1 year.
[tex]\bf ~~~~~~ \textit{Simple Interest Earned}
\\\\
I = Prt\qquad
\begin{cases}
I=\textit{interest earned}\to &\$5000\\
P=\textit{original amount deposited}\\
r=rate\to 8\%\to \frac{8}{100}\to &0.08\\
t=years\to &1
\end{cases}
\\\\\\
5000=P(0.08)(1)\implies \cfrac{5000}{(0.08)(1)}=P\implies 62500=P[/tex]
how about for for $4000 at 8% for 2 years?
[tex]\bf ~~~~~~ \textit{Simple Interest Earned}
\\\\
I = Prt\qquad
\begin{cases}
I=\textit{interest earned}\to &\$4000\\
P=\textit{original amount deposited}\\
r=rate\to 8\%\to \frac{8}{100}\to &0.08\\
t=years\to &2
\end{cases}
\\\\\\
4000=P(0.08)(2)\implies \cfrac{4000}{(0.08)(2)}=P\implies 25000=P[/tex]
how about for $8000 at 8% for 5 years?
[tex]\bf ~~~~~~ \textit{Simple Interest Earned}
\\\\
I = Prt\qquad
\begin{cases}
I=\textit{interest earned}\to &\$8000\\
P=\textit{original amount deposited}\\
r=rate\to 8\%\to \frac{8}{100}\to &0.08\\
t=years\to &5
\end{cases}
\\\\\\
8000=P(0.08)(5)\implies \cfrac{8000}{(0.08)(5)}=P\implies 20000=P[/tex]
