Question

scott invested a total of 5900 at two separate banks. one bank pays simple interest of 10% per year while the other pays simple interest at a rate of 6% per year. if scott earned $478 in interest during a single year, how much did he have on deposit in each bank?

Answer 1

Scott invested:

$3,100 at bank 1

$2,800 at bank 2

Explanation:

Use formula

`I=P\cdot r \cdot t,`

where

I = interest,

P = principal,

t = time,

r = rate (as decimal)

Let $x be the amount of money Scott invested at bank 1, then $(5,900-x) is his investment at bank 2

Bank 1:

`P_1=x\\ \\r_1=0.1\\ \\t_1=1\\ \\I_1=P_1\cdot r_1\cdot t_1=x\cdot 0.1\cdot 1=0.1x`

Bank 2:

`P_2=(5,900-x)\\ \\r_2=0.061\\ \\t_2=1\\ \\I_2=P_2\cdot r_2\cdot t_2=(5,900-x)\cdot 0.06\cdot 1=0.06(5,900-x)`

Total interest = $478, then

`I_1+I_2=478\\ \\0.1x+0.06(5,900-x)-478\\ \\10x+6(5,900-x)=47,800\\ \\10x+35,400-6x=47,800\\ \\10x-6x=47,800-35,400\\ \\4x=12,400\\ \\x=3,100\\ \\5,900-x=5,900-3,100=2,800`