Question

Cyndi wants to invest $50,000. She is advised to invest in three types of accounts: one paying 3%, one paying 5.5%, and one paying 9% simple interest per year. Cyndi wants to put twice as much in the lowest-yielding account as in the highest yielding account. How much should she invest in each account to achieve a total annual return of $2540?

Answer 1

Explanation:

Let's denote the amounts Cyndi invests in the three accounts as follows:

Let \( x \) be the amount invested in the account with a 9% interest rate.

Then, \( 2x \) is the amount invested in the account with a 5.5% interest rate (twice as much as the amount in the 9% account).

Finally, \( 3x \) is the amount invested in the account with a 3% interest rate (three times as much as the amount in the 9% account).

The total annual return can be expressed as the sum of the returns from each account:

\[ 0.09x + 0.055 \times 2x + 0.03 \times 3x = 2540 \]

Now, we can solve this equation to find the value of \( x \):

\[ 0.09x + 0.11x + 0.09x = 2540 \]

Combining like terms:

\[ 0.29x = 2540 \]

Now, solve for \( x \):

\[ x = \frac{2540}{0.29} \]

\[ x \approx 8758.62 \]

Now that we have the value of \( x \), we can find the amounts invested in each account:

- Amount in the 9% account: \( x \) dollars, which is approximately $8758.62.

- Amount in the 5.5% account: \( 2x \) dollars, which is approximately $17517.24.

- Amount in the 3% account: \( 3x \) dollars, which is approximately $26275.86.

Therefore, Cyndi should invest $8758.62 in the account with a 9% interest rate, $17517.24 in the account with a 5.5% interest rate, and $26275.86 in the account with a 3% interest rate to achieve a total annual return of $2540.