aliya deposited half as much money in a savings account earning 2% simple interest as she invested in a…

Explanation:

Step1: Define variables

Let $x$ be the amount invested in the money - market account. Then the amount invested in the savings account is $\frac{1}{2}x$.

Step2: Calculate the interest from each account

The interest formula for simple - interest is $I = Prt$. Since $t = 1$ year, the interest from the money - market account $I_1$ with a rate $r_1=3.1%=0.031$ is $I_1 = 0.031x$. The interest from the savings account $I_2$ with a rate $r_2 = 2%=0.02$ is $I_2=0.02\times\frac{1}{2}x=0.01x$.

Step3: Set up an equation for the total interest

The total interest $I = I_1+I_2$. We know that $I = 262.40$. So, $0.031x+0.01x=262.40$.

Step4: Combine like terms

Combining the $x$ terms on the left - hand side gives $(0.031 + 0.01)x=262.40$, which simplifies to $0.041x = 262.40$.

Step5: Solve for $x$

Dividing both sides of the equation $0.041x = 262.40$ by $0.041$, we get $x=\frac{262.40}{0.041}=6400$.

Step6: Find the amount invested in the savings account

The amount invested in the savings account is $\frac{1}{2}x$. Substituting $x = 6400$, we get $\frac{1}{2}\times6400 = 3200$.

Answer:

3200