Questions: 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. She deposited at 1.5% and at 2%

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.

She deposited at 1.5% and at 2%

Transcript text: 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 $\$ 825$. She deposited $\$$ $\square$ at $1.5 \%$ and $\$$ $\square$ at $2 \%$

Solution

Solution Steps

To solve this problem, we need to set up a system of linear equations based on the given information. Let $ x $ be the amount deposited at 1.5% interest and $ y $ be the amount deposited at 2% interest. We know that the total interest income is $825. We also know that twice as much is deposited at 2% as at 1.5%. This gives us two equations:

$ 0.015x + 0.02y = 825 $
$ y = 2x $

We can solve these equations simultaneously to find the values of $ x $ and $ y $.

Step 1: Define Variables and Equations

Let $ x $ be the amount deposited at $ 1.5\% $ interest and $ y $ be the amount deposited at $ 2\% $ interest. We are given the following information:

The total annual interest income is $ \$825 $.
Twice as much is deposited at $ 2\% $ as at $ 1.5\% $.

This gives us the following system of equations: \[ 0.015x + 0.02y = 825 \] \[ y = 2x \]

Step 2: Substitute and Solve

Substitute $ y = 2x $ into the first equation: \[ 0.015x + 0.02(2x) = 825 \] \[ 0.015x + 0.04x = 825 \] \[ 0.055x = 825 \] \[ x = \frac{825}{0.055} = 15000 \]

Step 3: Calculate $ y $

Using $ y = 2x $: \[ y = 2 \times 15000 = 30000 \]