Question

A new business borrows $320,000 at a yearly simple interest rate of 7%.

The total
amount the company repays for the loan and interest is $678,400. How long did it
take to pay off the loan? Pls help Mee!!

Answer 1

`~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 678400\\ P=\textit{original amount deposited}\dotfill & \$320000\\ r=rate\to 7\%\to (7)/(100)\dotfill &0.07\\ t=years \end{cases} \\\\\\ 678400 = 320000[1+(0.07)(t)] \implies \cfrac{678400}{320000}=1+0.07t\implies \cfrac{53}{25}=1+0.07t \\\\\\ \cfrac{53}{25}-1=0.07t\implies \cfrac{28}{25}=0.07t\implies \cfrac{(23)/(25)}{0.07}=t\implies \boxed{16=t}`