Question

Ms. Wilson invested $11.000 in two accounts, one yielding 8% interest and the other yielding 12%. If she received a total of $1,080 in interest at the end of the year how much did she invest in each account?

Answer 1

8% account - $6000
12% account - $5000

Explanation:

Let's call the money invested in the 8% account `a` and the money in the 12% account `b`.

We know that `a + b = 11000`.

To work out the interest, let's convert the percentages to decimals.

`8% = 0.08 and 12% = 0.12`

So `0.08a + 0.12b = 1080`

We now have a system of simultaneous equations, I'm going to solve via substitution.

`a = (1080-0.12b)/(0.08)`

`(1080-0.12b)/(0.08) + b = 11000`

Multiply both sides by `0.08`

`1080 - 0.12b + 0.08b = 11000*0.08`

`0.04b = 1080 - 11000*0.08`

`b = (1080-11000*0.08)/(0.04) = 5000`

`a+b = 11000 implies a = 6000`