Question

You invested $25,000 in two

accounts paying 9% and 8%
annual interest. If the total interest
earned for the year is $2100 how
much was invested of each rate?

Answer 1

let x be the capital invested in the 9% account

let y be the capital invested in the 8% account

let j be the interest earned from the 9% account

let k be the interest earned from the 8% account

`j = xi_(1)n \: \: \: (n = 1 \: year)\\ j = x( (9)/(100))(1) = 0.09x`

`k =yi_(2)n \: \: \: \: (n = 1 \: year) \\ k = y( (8)/(100) )(1) = 0.08y`

But the total interest made is 2100 $, hence:

`\: \: \: \: \: \: \: j + k = 2100 \\ 0.09x + 0.08y = 2100`

And the total capital invested is 25000 $

`x + y = 25000`

System of 2 equations and two unknowns:

`0.09x + 0.08y = 2100 \\ x + y = 25000 \\ \\ \: \: \: \: (x,y)=(10000,15000)`