Question

sarah ontkean is the manager of a mutual fund. she placed 30% of the funds available cash in a 6% annual simple - interest account, 25% in 8% corporate bonds, and the remainder in a money - market fund earning 7.5% annual simple interest. the total annual interest earned from the investments was $31,570. find the total amount invested.

Explanation:

Step1: Let the total amount invested be $x$.

The amount in the 6% account is $0.3x$, the amount in 8% corporate - bonds is $0.25x$, and the amount in the 7.5% money - market fund is $(1 - 0.3 - 0.25)x=0.45x$.

Step2: Calculate the interest from each investment.

The interest from the 6% account is $I_1 = 0.06\times0.3x=0.018x$. The interest from the 8% corporate bonds is $I_2 = 0.08\times0.25x = 0.02x$. The interest from the 7.5% money - market fund is $I_3=0.075\times0.45x = 0.03375x$.

Step3: Set up an equation for the total interest.

The total interest $I = I_1+I_2 + I_3$. We know that $I = 31570$, so $0.018x+0.02x + 0.03375x=31570$.

Step4: Combine like terms.

$(0.018 + 0.02+0.03375)x=31570$, which simplifies to $0.07175x = 31570$.

Step5: Solve for $x$.

$x=\frac{31570}{0.07175}=440000$.

Answer:

$440000$