Question

What simple interest rate is needed for $6,000 to earn $1,000 in 15 months

Answer 1

let's recall that a year has 12 months, so 15  months is really 15/12 years.

$\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&\ 1000\\ P=\textit{original amount deposited}\dotfill & \ 6000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{15}{12}\dotfill &\frac{5}{4} \end{cases}$

$\bf 1000=(6000)r\left( \cfrac{5}{4} \right)\implies 1000=7500r\implies \cfrac{1000}{7500}=r\implies \cfrac{2}{15}=r \\\\\\ \stackrel{\textit{converting that to a percentage}}{\cfrac{2}{15}\cdot 100 = r\implies \cfrac{40}{3}=r}\implies \stackrel{\%~\hfill }{13.\overline{3}}=r$