Question

The principal "P" is borrowed and the​ loan's future value "A" at time "t" is given. Determine the​ loan's simple interest rate "r" to the nearest tenth of a percent. P=2500.00 A=2525.00 T=3 months

Answer 1

Now.... "t" is in years, 3months off 12 months is 3/12 years

$\bf \qquad \textit{Simple Interest Earned Amount}\\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\to &\ 2525\\ P=\textit{original amount deposited}\to& \ 2500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{3}{12}\to &\frac{1}{4} \end{cases}$

$\bf 2525=2500\left(1+r\cdot \frac{1}{4} \right)\implies \cfrac{2525}{2500}=1+\cfrac{1}{4}r\implies \cfrac{101}{100}=1+\cfrac{r}{4} \\\\\\ \cfrac{101}{100}-1=\cfrac{r}{4}\implies \cfrac{1}{100}=\cfrac{r}{4}\implies \cfrac{4}{100}=r\implies 0.04=r \\\\\\ \textit{to convert to percentage format}\implies 0.04\cdot 100\implies 4\%$