Question

Kian borrowed £1900 at a simple interest rate of 8% per year.

After a certain number of years, he owes a total of £2812 on this loan.
How many years have passed since he took out the loan?

Answer 1

`~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2812\\ P=\textit{original amount deposited}\dotfill & \$1900\\ r=rate\to 8\%\to (8)/(100)\dotfill &0.08\\ t=years \end{cases} \\\\\\ 2812=1900[1+(0.08)(t)]\implies \cfrac{2812}{1900}=1+0.08t\implies \cfrac{37}{25}=1+0.08t \\\\\\ \cfrac{37}{25}-1=0.08t\implies \cfrac{12}{25}=0.08t\implies \cfrac{ ~~ (12)/(25) ~~ }{0.08}=t\implies 6=t`