Question

In planning her retirement, Liza deposits some money at 2.5% interest, with twice as much deposited at 5.5%. Find the amount deposited at each rate if the total annual interest income is $1620.

Answer 1

Answer: Let's denote the amount of money Liza deposited at 2.5% interest as x dollars. According to the problem, she deposited twice as much, or 2x dollars, at 5.5% interest.

To calculate the interest income from each deposit, we can use the formula: Interest = Principal × Rate × Time.

For the deposit at 2.5% interest:

Interest_2.5% = x × 0.025.

For the deposit at 5.5% interest:

Interest_5.5% = 2x × 0.055.

According to the problem, the total annual interest income is $1620. So we can set up the following equation:

Interest_2.5% + Interest_5.5% = 1620.

Plugging in the expressions for the interest at each rate, we get:

x × 0.025 + 2x × 0.055 = 1620.

Simplifying the equation:

0.025x + 0.11x = 1620.

0.135x = 1620.

x = 1620 / 0.135.

x ≈ 12000.

Therefore, Liza deposited $12,000 at 2.5% interest, and twice as much, or $24,000, at 5.5% interest.