Question

Ben invests a total of $1000 in two accounts, one earning 5% annually and another earning 7% annually. His total annual return is $65. a. Using two variables, make a table representing the return on his investments. b. Write and solve a system of equations to determine the amount invested in each account. i. at 5% ii. at 7%

Answer 1

Ben invested $250 in the account with a 5% annual return and $750 in the account with a 7% annual return. This was determined by solving a system of equations derived from the info given about the total investment amount and the total annual interest earned.

Step-by-step explanation:

Investment Allocation Problem

Let's denote x as the amount invested at 5%, and y as the amount invested at 7%. According to the question, the total investment is $1000, which gives us our first equation:

x + y = 1000 (1)

The total annual return from both accounts is $65. Using the given interest rates, the return from the first account is 0.05x and from the second account is 0.07y. This gives us our second equation:

0.05x + 0.07y = 65 (2)

To find the amount invested in each account, we need to solve this system of equations. By multiplying equation (2) by 20 to get rid of the decimals, we get:

x + 1.4y = 1300 (3)

Subtracting equation (1) from equation (3) results in:

0.4y = 300 => y = 750

Now that we have the value for y, we can substitute it back into equation (1) to find x:

x + 750 = 1000 => x = 250

Therefore, Ben invested $250 at 5% and $750 at 7%.