Danielle invests part of her $5000 savings into a savings account at 3% and part into a GIC at 4% simple interest. If she earns $189.50 interest from her two investments, calculate how much she invested at each rate.
Let the amount invested in the savings account be x
The amount invested in the GIC will be $5000 - x
The interest earned from the savings account at 3% is x * 3/100
The interest earned from the GIC at 4% is (5000 - x) * 4/100
When you add the interest earned from both accounts, you get x * 3/100 + (5000 - x) * 4/100 = $189.5
Multiply through the parentheses to get x * 3/100 + 20000/100 - (x * 4/100) = $189.50
Multiply the denominators and organize the equation to get x * 3 + 20000 - 4x = $189.50 * 100
Combine like terms to get x * -1 + 20000 = $18950
Move the 20000 to the other side of the equation to get x * -1 = $18950 - 20000
Combine like terms to get x * -1 = -$1050
Divide both sides of the equation by -1 and simplify to get x = $1050
She invested $1050 at 3% interest and the rest at 4% interest, which is $5000 - $1050 = $<<5000-1050=3950>>3950. Answer: \boxed{1050, 3950}.
Let's assume Danielle invested x dollars in the savings account at 3% interest rate.
Therefore, she invested (5000 - x) dollars in the GIC at 4% interest rate.
We can calculate the interest earned from the savings account:
Interest from savings account = x * 0.03
We can also calculate the interest earned from the GIC:
Interest from GIC = (5000 - x) * 0.04
The total interest earned is given as $189.50, so we can set up the following equation:
Interest from savings account + Interest from GIC = 189.50
Substituting the above expressions, we have:
x * 0.03 + (5000 - x) * 0.04 = 189.50
Now, let's solve this equation step-by-step:
Step 1: Distribute the 0.04 to both terms inside the brackets:
0.03x + (5000 * 0.04 - 0.04x) = 189.50
Step 2: Simplify the expression:
0.03x + (200 - 0.04x) = 189.50
Step 3: Combine like terms:
0.03x + 200 - 0.04x = 189.50
Step 4: Move the constants to the other side of the equation:
-0.01x = 189.50 - 200
Step 5: Simplify the expression:
-0.01x = -10.50
Step 6: Divide both sides of the equation by -0.01 to solve for x:
x = -10.50 / -0.01
Step 7: Calculate the value of x:
x = 1050
Therefore, Danielle invested $1050 in the savings account at a 3% interest rate.
To find out how much she invested in the GIC, we can substitute the value of x back into the expression:
5000 - x = 5000 - 1050 = 3950
Therefore, Danielle invested $3950 in the GIC at a 4% simple interest rate.
To solve this problem, let's assume that Danielle invests x dollars into the savings account at 3% and y dollars into the GIC at 4%.
We know that the interest earned from the savings account is given by the formula:
Interest from savings account = (Principal × Rate × Time)
So, the interest earned from the savings account is (x × 0.03 × 1), since the time is not given.
Similarly, the interest earned from the GIC is given by:
Interest from GIC = (Principal × Rate × Time)
So, the interest earned from the GIC is (y × 0.04 × 1).
Given that the total interest earned from both investments is $189.50, we can write the equation:
Interest from savings account + Interest from GIC = Total interest earned
(x × 0.03 × 1) + (y × 0.04 × 1) = $189.50
Now, let's solve this equation to find the values of x and y.
0.03x + 0.04y = 189.50
We also know that Danielle invests a total of $5000, so we have another equation:
x + y = $5000
Now we have a system of two equations that we can solve simultaneously.
Using various methods such as substitution or elimination, let's solve these equations to find the values of x and y.