Question

Scott invested a total of S6300 at two separate banks One bank pays simple interest of 10% per year while the other pays simple interest at a rate of 7% per year. IfScott earned $534.00 in interest during a single year how much did he have on deposit in each bank?

Answer 1

Case: Simple Interest

Given:

total investment of S6300

One bank pays simple interest of 10% per year

the other bank pays simple interest at a rate of 7% per year

earned interest= $534.00

Required: To find the amount invested in each bank

Method:

Step 1: First let the investments in each bank be x and y.

Hence,

x + y= 6300

Step 2: Find the interest in each bank

`\begin{gathered} I_x=PRT \\ =x(0.1)(1) \\ =0.1x \end{gathered}`
`\begin{gathered} I_y=PRT \\ =y(0.07)(1) \\ =0.07y \end{gathered}`

Step 4: Total interest earned

`\begin{gathered} I_x+I_y=534 \\ 0.1x+0.07y=534 \end{gathered}`

Step 5: Solve the system of equation

`\begin{gathered} x+y=6300..(1) \\ 0.1x+0.07y=534..(2) \\ Using\text{ Elimination method, Multiply \lparen1\rparen by 0.1} \\ 0.1x+0.1y=630 \\ 0.1x+0.07y=534 \\ Subtracting \\ 0.1y-0.07y=630-534 \\ 0.03y=96 \\ y=3200 \end{gathered}`

Step 6: Plug the value of y= 3200 in the equation (1)

x + y= 6300

x + 3200= 6300

x= 6300 - 3200

x= 3100

Final answer:

The investments are

$3100 for 10% AND

$3200 for 7%