Question

Donna invested money in two accounts. One paying 4% simple interest and the other paying 3% simple interest. She invested $3000 more in the 4% account than in the 3% account. If she received $960 in interest at the end of 1 year, how much did she invest in each account?

a) $6,000 in the 4% account and $3,000 in the 3% account.
b) $9,000 in the 4% account and $6,000 in the 3% account.
c) $12,000 in the 4% account and $9,000 in the 3% account.
d) $3,000 in the 4% account and $2,000 in the 3% account.

Answer 1

The correct answer is c) $12,000 in the 4% account and $9,000 in the 3% account. By setting up an equation using simple interest formulas and solving for x, the amounts invested in each account can be determined.

Step-by-step explanation:

The question involves solving a system of linear equations that stem from the scenario where Donna invested her money in two different accounts with different simple interest rates, and she needs to find out the total amount invested in each account.

Let the amount invested at 3% be x dollars, then the amount at 4% would be x + $3,000 because it's given that she invested $3,000 more in the 4% account. After one year, the interest from the 3% account will be 0.03x, and from the 4% account will be 0.04(x + $3,000). According to the problem, the total interest is $960, which gives us the equation:

0.03x + 0.04(x + 3000) = 960

Solving the equation:

• 0.03x + 0.04x + 120 = 960
• 0.07x + 120 = 960
• 0.07x = 840
• x = $12,000
  

Therefore, the amount invested at 3% is $12,000, and the amount invested at 4% is $12,000 + $3,000 = $15,000.

So, the correct choice is c) $12,000 in the 4% account and $9,000 in the 3% account.