What annual installment will discharge a debt of $10,920$ due in $3$ years at $12\%$ simple interest?

Let the annual installment be $x$.
The debt is settled at the end of $3$ years.
The first installment is paid at the end of the 1st year, so it earns interest for $(3-1)=2$ years.
The second installment is paid at the end of the 2nd year, so it earns interest for $(3-2)=1$ year.
The third installment is paid at the end of the 3rd year, so it earns interest for $(3-3)=0$ years.

The sum of all installments with their respective accumulated simple interest equals the total debt:

$$x+\left(x+\frac{x\times 12\times 1}{100}\right)+\left(x+\frac{x\times 12\times 2}{100}\right)=10,920$$

$$x+1.12x+1.24x=10,920$$

$$3.36x=10,920$$

$$x=\frac{10,920}{3.36}=3,250$$

Therefore, the annual installment is $3,250$.