Question

In planning her​ retirement, Liza deposits some money at 1.5 1.5​% ​interest, with twice as much deposited at 2.5 2.5​%. Find the amount deposited at each rate if the total annual interest income is ​$ 780 780.

Answer 1

Answer:Liza deposited $12000 at 1.5% and $24000 at 2.5%

Step-by-step explanation:

Let x represent the amount that she deposited at 1.5% interest.

Let y represent the amount that she deposited at 2.5% interest.

In planning her​ retirement, Liza deposits some money at 1.5​% ​interest, with twice as much deposited at 2.5%. This means that

y = 2x

The formula for determining simple interest is expressed as

I = PRT/100

Considering the account paying 1.5% interest,

P = $x

T = 1 year

R = 1.5℅

I = (x × 1.5 × 1)/100 = 0.015x

Considering the account paying 2.5% interest,

P = $y

T = 1 year

R = 2.5℅

I = (y × 2.5 × 1)/100 = 0.025y

if the total annual interest income is ​$780 , it means that

0.015x + 0.025y = 780 - - - - - - - - - -1

Substituting y = 2x into equation 1, it becomes

0.015x + 0.025 × 2x = 780

0.015x + 0.05x = 780

0.065x = 78

x = 780/0.065

x = 12000

y = 2x = 12000 × 2

y = 24000