How to solve the given problem of simple interest?

Question

The problem statement is:

What annual instalment will discharge a debt of 1092 due in 3 years at 12% simple interest?

Now, what I know is

Simple interest =( principal* Rate per annum*Time in years)/(100)

Here, R= 12℅ ,T=3 years but I don't understand how to move forward.I am not getting the meaning of the problem statement.

I am adding the solution from one book for the given question but I don't understand it. So can anyone explain it? Or can anyone give there own solution to the given question?

Answer 1

The problem statement is stating that one will make one payment each year towards the debt.

As I read it, it sounds like the annual installment should be the same from year to year.

Answer 2

Your repayment amount yields an interest of 12% per year. The last installment (the third)does not fetch any interest. The second installment will give 12% interest for one year. That is, the amount $x$ paid at the end of second year would be $x + \frac{x \times 12}{100}$ at the end of third year. The installment you paid at the end of first year will fetch interest for 2 years. Thus it would be $x + \frac{2 \times x \times 12}{100}$. Thus we must have \begin{align*} x \text{ (last installment) } + \left(x + \frac{x \times 12}{100}\right) \text{ (second installment) } + x + \frac{2 \times x \times 12}{100} \text{ (first installment) } = 1092 \end{align*} The rest is clear to you, I suppose.