Question

John borrows $2,500 from his dad, who feels it is best to charge him interest. Six months later, John repays his dad the loan plus interest, a total of $2,588. What is the annual interest rate on the loan?

Answer 1

well, we know that a year has 12 months, so 6 months is really just 6/12 of a year.

`~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 2588\\ P=\textit{original amount deposited}\dotfill & \$2500\\ r=rate\to r\%\to (r)/(100)\\ t=years\to (6)/(12)\dotfill &(1)/(2) \end{cases}`

`2588 = 2500[1+((r)/(100))((1)/(2))] \implies \cfrac{2588}{2500}=1+\cfrac{r}{200}\implies \cfrac{647}{625}=\cfrac{200+r}{200} \\\\\\ \cfrac{(200)(647)}{625}=200+r\implies \cfrac{(200)(647)}{625}-200=r\implies \boxed{7.04=r}`