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 (r)/(100)\\ t=years\to (3)/(12)\to &(1)/(4) \end{cases}`


`\bf 2525=2500\left(1+r\cdot (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\%`