Question

After 6 months the simple interest earned annually on an investment of $6,000 was $463. Find the interest rate to the nearest tenth of a percent.

Answer 1

Keeping in mind that 6 months is not even a year, since there are 12 months in a year, then 6 months is 6/12, or 1/2 a year, thus

$\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\ 463\\ P=\textit{original amount deposited}\to& \ 6000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to &\frac{1}{2} \end{cases} \\\\\\ 463=(6000)(r)\left( \frac{1}{2} \right)\implies \cfrac{463}{(6000)\left( \frac{1}{2} \right)}=r\implies 0.154\approx r \\\\\\ r\%\approx 100\cdot 0.154\implies r\approx \stackrel{\%}{15.4}$