Question

sarah ottosen 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 $31,370. find the total amount invested.

Explanation:

Step1: Calculate the percentage of the third - investment

The first investment is 30% and the second is 25%. The percentage of the third investment is $100-(30 + 25)=45\%$.

Step2: Let the total amount invested be $x$.

The interest from the first investment is $0.3x\times0.06$, from the second is $0.25x\times0.08$, and from the third is $0.45x\times0.075$.

Step3: Set up the interest - equation

The total annual interest is $31170$. So, $0.3x\times0.06+0.25x\times0.08 + 0.45x\times0.075=31170$.
First, calculate each term:
$0.3x\times0.06 = 0.018x$, $0.25x\times0.08=0.02x$, $0.45x\times0.075 = 0.03375x$.
The equation becomes $0.018x+0.02x + 0.03375x=31170$.
Combine like - terms: $(0.018 + 0.02+0.03375)x=31170$.
$0.07175x=31170$.

Step4: Solve for $x$

Divide both sides of the equation by $0.07175$: $x=\frac{31170}{0.07175}=434425.09$.

Answer:

$434425.09$