Cyndee wants to invest $50,000. Her financial planner advises her to invest in three types of accounts: one paying 3%, one paying 5 1/2%, and one paying 6% simple interest per year. Cyndee wants to put twice as much in the lowest-yielding, least-risky account as in the highest-yielding account. How much should she invest in each account to achieve a total annual return of $2165?

Well, Cyndee certainly has some interesting decisions to make! With those interest rates, it sounds like she'll be keeping us on our toes. Let's see if we can help her out with some clownish calculations.

To start, let's call the amount invested in the highest-yielding account "x". Since she wants to put twice as much in the lowest-yielding account, we'll call that amount "2x". Now, we can set up an equation to solve for x.

First, we'll calculate the interest earned from each account. The account paying 3% will earn 0.03x, the account paying 5 1/2% will earn 0.055x, and the account paying 6% will earn 0.06(2x).

Now, the sum of these three interest amounts should be equal to the total annual return of $2165. So we have the equation:

0.03x + 0.055x + 0.06(2x) = 2165

Now it's time for some clownish calculations! Let's solve this equation and find out how much Cyndee should invest in each account.

0.03x + 0.055x + 0.12x = 2165
0.205x = 2165
x = 2165 / 0.205
x ≈ 10585.37

Now, let's find out how much she should invest in the lowest-yielding account, which we called "2x". Plugging in the value of x:

2x ≈ 2 * 10585.37 ≈ 21170.74

So Cyndee should invest approximately $10,585.37 in the highest-yielding account and approximately $21,170.74 in the lowest-yielding account.

Now, where does the last account come in? Well, we've only solved for two accounts so far. If she wants to invest in three accounts, she can put the remaining amount ($50,000 - $10,585.37 - $21,170.74) in the 6% account.

Hope that helps, and remember, investing can be a bit of a circus sometimes, but with a little bit of math and a lot of laughter, we'll all get through it!

To solve this problem, we can use a system of equations.

Let's represent the amount Cyndee invests in the highest-yielding account as "x".
Then, the amount she invests in the lowest-yielding account would be "2x" (twice as much).
Finally, the remaining amount she invests in the account paying 5 1/2% would be "50000 - 3x - 2x" (the sum invested in the other two accounts subtracted from the total amount).

The total return from the highest-yielding account at 6% interest would be 0.06x.
The total return from the lowest-yielding account at 3% interest would be 0.03(2x).
The total return from the account paying 5 1/2% interest would be 0.055(50000 - 3x - 2x).

Based on the problem statement, the sum of these returns should be $2,165:

0.06x + 0.03(2x) + 0.055(50000 - 3x - 2x) = 2165

Simplifying the equation:

0.06x + 0.06x + 0.055(50000 - 5x) = 2165
0.12x + 0.055(50000 - 5x) = 2165
0.12x + 2750 - 0.275x = 2165

Combining like terms:

0.12x - 0.275x = 2165 - 2750
-0.155x = -585

Solving for x:

x = -585 / -0.155
x = 3,774.19

Since Cyndee can't invest a negative amount, we can conclude that she should invest $3,774.19 in the highest-yielding account.

Now, we can find the amounts she should invest in the other two accounts:

Investment in the lowest-yielding account: 2x = 2 * 3,774.19 = $7,548.38
Investment in the account paying 5 1/2%: 50000 - 3x - 2x = 50,000 - 3 * 3,774.19 - 2 * 7,548.38 = $33,677.23

So, Cyndee should invest approximately $3,774.19 in the highest-yielding account, $7,548.38 in the lowest-yielding account, and $33,677.23 in the account paying 5 1/2% interest to achieve a total annual return of $2,165.

To determine the amounts that Cyndee should invest in each account, we can set up a system of equations based on the given information. Let's assign variables to the unknowns:

Let x represent the amount invested in the highest-yielding account (6% interest rate).
Since Cyndee wants to put twice as much in the lowest-yielding account, let's assign 2x to the amount invested in the lowest-yielding account (3% interest rate).
Finally, let's denote y as the amount invested in the remaining account (5 1/2% interest rate).

Here's the system of equations based on the conditions given:

Equation 1: x + 2x + y = $50,000 (the total amount invested is $50,000)
Equation 2: 0.06x + 0.03(2x) + 0.055y = $2,165 (the total annual return is $2,165)

To solve this system of equations, we can substitute Equation 1 into Equation 2 and solve for x:

0.06x + 0.03(2x) + 0.055y = $2,165
0.06x + 0.06x + 0.055y = $2,165
0.12x + 0.055y = $2,165

Substitute x = 2x into the equation above:

0.12(2x) + 0.055y = $2,165
0.24x + 0.055y = $2,165

Substitute 3x for the expression 0.24x:

3x + 0.055y = $2,165

Now substitute the value of 2x from Equation 1:

3x + 0.055y = $2,165
3(2x) + 0.055y = $2,165
6x + 0.055y = $2,165

Substitute the value of 50,000 - 3x from Equation 1:

6x + 0.055y = $2,165
6x + 0.055(50,000 - 3x) = $2,165

Simplify and solve for x:

6x + 0.055(50,000 - 3x) = $2,165
6x + 2,750 - 0.165x = $2,165
5.835x + 2,750 = $2,165
5.835x = $2,165 - $2,750
5.835x = -$585
x = -$585 / 5.835
x ≈ -$100

Unfortunately, the result for x is negative, which doesn't make sense in this context. It seems that the given information or the problem set up might have an error. Please double-check the information and try again.

P Dollars @ 6%, 2P Dollars @ 3%, (50,000-3P) @ 5.5

0.06P + 0.03(2P) + 0.055(50,000-3P) = 2165.

0.06P + 0.06P + 2750 - 0.165P = 2165, -.045P = 2165-2750 = -585, P = $13,000 @ 6%.

2P = $26,000 @ 3%.

(50,000-39,000) = $11,000 @ 5.5%.