Question

A loan of $25000 has an annual simple interest rate of 5.5%. The total cost of the loan is $38750. How many years does it take to repay the loan

Answer 1

`~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$38750\\ P=\textit{original amount deposited}\dotfill & \$25000\\ r=rate\to 5.5\%\to (5.5)/(100)\dotfill &0.055\\ t=years \end{cases} \\\\\\ 38750=25000[1+(0.055)(t)] \implies \cfrac{38750}{25000}=1+0.055t\implies \cfrac{31}{20}=1+0.055t \\\\\\ \cfrac{31}{20}-1=0.055t\implies \cfrac{11}{20}=0.055t\implies \cfrac{11}{20(0.055)}=t\implies 10=t`