Question

Hattie had $2,100 to invest and wants to earn 3.8% interest per year. She will put some of the money into an account that earns 2.8% per year and the rest into an account that earns 4.2% per year. How much money should she put into each account?

a. $900 in 2.8%, $1,200 in 4.2%
b. $1,200 in 2.8%, $900 in 4.2%
c. $1,500 in 2.8%, $600 in 4.2%
d. $600 in 2.8%, $1,500 in 4.2%

Answer 1

Hattie should invest $1,200 at 2.8% interest and $900 at 4.2% interest to achieve an overall annual interest rate of 3.8% on her $2,100 investment. This corresponds to option b.

Step-by-step explanation:

Hattie wants to invest $2,100 to earn an overall interest rate of 3.8% per year by distributing the money into two accounts with different interest rates of 2.8% and 4.2%. To solve this, let's assign x to the amount of money invested at 2.8% and y to the amount of money invested at 4.2%. We can set up the following system of equations:

• x + y = 2100 (total amount of money Hattie has)
• 0.028x + 0.042y = 2100 * 0.038 (total desired interest from $2,100)

Solving the system of equations, we find that x = $1,200 should be invested at 2.8%, and y = $900 should be invested at 4.2%, which corresponds to option b.