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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?

Solution given in the book is

Martin Sleziak
  • 53,687
sagar
  • 405

2 Answers2

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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.

  • but I don't understand if it is the problem of simple interest, the installment for each year should be same . but here in the solution, every year installment is different. Why is it so? – sagar Jul 19 '16 at 12:44
  • Instalment is the same, $x$. It earns interest every year. It is like putting $X$ $ every year for three years and withdrawing the money at the end of third year and paying the debt. –  Jul 20 '16 at 00:51
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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.

Zach Zundel
  • 123
  • yes,they have asked for the each instalment. And they have given answer : each installment= 325. But I don't know how they got the given answer. Also, What is "amount of principal" here? And what is 1092 in the given question? – sagar Jul 18 '16 at 10:02
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    The total amount comes to only 975, How can it clear a debt of 1092$? –  Jul 18 '16 at 10:05
  • Perhaps this question and answer can help you. http://math.stackexchange.com/questions/838691/what-annual-installment-will-discharge-a-certain-debt – Zach Zundel Jul 18 '16 at 10:07
  • @Muralidharan I have added the image in which the solution for the question is given. But I don't understand it. If you understand it, will you please explain me. – sagar Jul 18 '16 at 10:18