Question

Last year, Bob had $10,000 to invest. He invested some of it in an account that paid 5% simple interest per year, and he invested the rest in an account thatpaid 6% simple interest per year. After one year, he received a total of $540 in interest. How much did he invest in each account?

Answer 1

To know how much Bob invested in the account that paid 5%, we shall use the relation below

`(5)/(100)x+(6)/(100)(10000-x)=540`

Where x is the amount invested in an account that paid 5% simple interest and (10000 - x) represents, the amount invested in an account that paid 6% simple interest.

`\begin{gathered} \Rightarrow0.05x+0.06(10000-x)=540 \\ 0.05x+600-0.06x=540 \\ 0.05x-0.06x=540-600 \\ -0.01x=-60 \\ x=(60)/(0.01) \\ x=6000 \end{gathered}`

Therefore, $6,000 is the amount invested in the account that paid 5% simple interest

Now, the amount invested in an account that paid 6% simple interest would be

`\begin{gathered} =10000-6000 \\ =4000 \end{gathered}`

∴ $4,000 is invested in an account that paid 6% simple interest.