Question

How long will it take for $800 to increase to $992 if invested at 4% per annum simple interest?

Answer 1

`~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 992\\ P=\textit{original amount deposited}\dotfill & \$800\\ r=rate\to 4\%\to (4)/(100)\dotfill &0.04\\ t=years \end{cases} \\\\\\ 992 = 800[1+(0.04)(t)] \implies \cfrac{992}{800}=1+0.04t\implies \cfrac{31}{25}=1+0.04t \\\\\\ \cfrac{31}{25}-1=0.04t\implies \cfrac{6}{25}=0.04t\implies \cfrac{6}{25(0.04)}=t\implies 6=t`

Answer 2

it will take 6 years.

Explanation:

4% of 800 is 32. 992 - 800 is 192. 192 / 32 is 6. So therefore it will take 6 years. :)