in planning her retirement, liza deposits some money at 1.5 % interest, with twice as much deposited at 2 %. find the amount deposited at each rate if the total annual interest income is $825.

Let us assume $x is deposit at 1.5% interest.

At the rate 2% deposited amount is twice of the amount deposited at 2%.

Therefore, at the rate 2% deposited amount = $2x.

Total interest earned by both different deposited amount at the rate 1.5% and at the rate 2% = $825.

We can setup an eqation now,

Interest earned on $x at 1.5% + interest earned on $2 at 2% = $825.

1.5% of x + 2% of 2x = 825

Percentage could be written in decimals by dividing by 100.

Therefore, 1.5% = 1.5 / 100 = 0.015 and 2% = 2/100 = 0.02.

We could rewrite above equation as,

0.015*x + 0.02 * 2x = 825

0.015x + 0.04x = 825

Adding 0.015x + 0.04x, we get 0.055x.

So, 0.055x=825.

Dividing both sides by 0.055.

0.055x/0.055=825/0.055.

x = $15000.

2x = 2 * 15000 = $30000

Therefore,

$15000 deposited at 1.5% and $30000 deposited at 2%.