Question

A man invests a certain amount of money at 2% and $800 more than that amount in another account at 4% interest. At the end of the one year, he earned $112 in interest. How much money was invested in each account?

Answer 1

`$1,333.33` invested at 2%
`$2,1333.33` invested at 4%

Explanation:

As the time is only 1 year, it does matter whether it is simple or compound interest.

Define each amount of money using a variable.

Let the smaller amount of money (at 2%) be `x`
The larger amount (at 4%) is `x +800`

The interest on the first amount = `(x xx 2)/100 = color(red)((2x)/100)`

The interest on the larger amount = `color(blue)(((x+800) xx4)/100)`

The total interest is `$112`

`color(red)((2x)/100 )+ color(blue)((4(x+800))/100) = 112`

`(2x+4x+3200)/100 = 112`

`(6x +3200)/100 = 112" "larr xx 100`

`6x +3200 = 11200`

`6x = 8000`

`x = $1,333.33`

`x+ 800= $2,133.33`