Question

Scott invested a total of $6300 at two separate banks. One bank pays simple interest of 10% per year while the other pays simple interest at a rate of 9% per year. If Scott eamed $598.00 in interest during asingle year, how much did he have on deposit in gach bank?

Answer 1

Step-by-step explanation: Scott Invested in two banks, and each bank paid 9% and 10% yearly interest. the total amount invested was $6300 and the Interest earned in the first year is $598. We have to find the amount invested in each bank.

Mathematical Formula:

let us say that amount x was invested in the first bank and amount y was invested in the second bank, considering this we can write the following equation for the total money invested:

`\begin{gathered} x+y=\$6300\Rightarrow(1) \\ \end{gathered}`

Similarly, the following is the equation for the total Interest earned in the first year.

`(0.1)x+(0.09)y=\$598\Rightarrow(2)`

Equation (1) and (2) are two linear simultaneous equations:

`\begin{cases}x+y={6300} \\ (0.1)x+(0.09)y={598}\end{cases}`

The graphical solution to the above system is as follows:

Therefore the amount invested in each bank is:

`\begin{gathered} x=\$3,100 \\ y=\$3,200 \\ \\ \because\rightarrow \\ x+y=\$3,100+3,200=\$6,300\rightarrow\text{ \lparen Checks out\rparen} \end{gathered}`

Scott invested $3,100 in the first bank and in the second bank, he invested $3,200.