Question

A person wants to invest $150 000 dollars and the credit union offers an interest of 7.5% per annum. (Calculate how many years it will take for the AMOUNT of money to cross $200 000 when using simple interest.​

Answer 1

`~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$200000\\ P=\textit{original amount deposited}\dotfill & \$150000\\ r=rate\to 7.5\%\to (7.5)/(100)\dotfill &0.075\\ t=years \end{cases}`

`200000=150000[1+(0.075)(t)] \implies \cfrac{200000}{150000}=1+0.075t \\\\\\ \cfrac{4}{3}=1+0.075t\implies \cfrac{4}{3}-1=0.075t\implies \cfrac{1}{3}=0.075t \\\\\\ \cfrac{1}{3(0.075)}=t\implies 4.44\approx t\qquad \textit{about 4 years and 160 days}`