SOLUTION:
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
[tex]\begin{gathered} I_x=PRT \\ =x(0.1)(1) \\ =0.1x \end{gathered}[/tex][tex]\begin{gathered} I_y=PRT \\ =y(0.07)(1) \\ =0.07y \end{gathered}[/tex]Step 4: Total interest earned
[tex]\begin{gathered} I_x+I_y=534 \\ 0.1x+0.07y=534 \end{gathered}[/tex]Step 5: Solve the system of equation
[tex]\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}[/tex]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%
