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ruslelena [56]
2 years ago
6

If $8700 is invested at 3% annual simple interest, how much should be invested at 6% annual simple interest so that the total ye

arly income for both investments is $393?
Mathematics
1 answer:
True [87]2 years ago
6 0
First off, see  how much 8700 as principal, yields at 3% APR
that is \bf \qquad \textit{Simple Interest Earned}\\\\
I = Prt\qquad 
\begin{cases}
I=\textit{interest earned}\\
P=\textit{original amount deposited}\to& \$8700\\
r=rate\to 3\%\to \frac{3}{100}\to &0.03\\
t=years\to &1
\end{cases}

it will yield some amount

subtract that amount from 393
the difference is how much the yield will be on the 6% investment
so

\bf \qquad \textit{Simple Interest Earned}\\\\
I = Prt\quad 
\begin{cases}
I=\textit{interest earned}\\
P=\textit{original amount deposited}\to& \$8700\\
r=rate\to 3\%\to \frac{3}{100}\to &0.03\\
t=years\to &1
\end{cases}
\\\\\\
\implies \boxed{?}\\\\
-----------------------------\\\\
\textit{how much to invest at 6\%?}
\\\\\\


\bf \qquad \textit{Simple Interest Earned}\\\\
(393-\boxed{?}) = Prt\quad 
\begin{cases}
I=\textit{interest earned}\\
P=\textit{original amount deposited}\to& \$\\
r=rate\to 6\%\to \frac{6}{100}\to &0.06\\
t=years\to &1
\end{cases}
\\\\\\
\textit{solve for "P", to see how much should the Principal be}\\\\
\textit{keep in mind that }P+\boxed{?}=393\leftarrow \textit{both yields added}
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