Aptitude - True Discount - Discussion

In the first attempt, I also calculated the answer Rs. 9222.17 but this approach is wrong.

Because merchant makes a deal for one year and trader is paying before the due date so we have to subtract interset on that amount for 9 months.

The amount that trader has to pay after 1 year, he settles it after 3 months i.e. 9 months before the due date.

So PW of the amount now after 3 months i.e. 9 months before the actual payment as the deal is done can be calculated simply as given in the solution.

I didn't understand this, please explain me.

It would be 10028/(1.12)^(9/12) = 9210.87.

Why 100 is added in the denominator?

Present worth = not given.

p.w + t.d = 10028 given --> 1
td=p.w*n*r/100;

From above find p.w first
i.e, t.d=p.w*1*12/100 --> (2)
t.d=0.12p.w; put in (1).
p.w=8953.57.

Now from p.w find t.d for 3 months which is 268.605 --> formula given in(2))
Amount should pay = total=p.w+t.d for 3 month.
= 8953.571+268.805 = 9222.17.

CONCEPT OF THE QUESTION:

As the trader is settling the account after 3 months, that means he will going to recognize the amount (INT + down pay) for 3 months.

Opinion: In this forum I've analyzed 2 ways of treating the question, both methods are like a integer line (negative to positive)

1 Method: (Positive one):

10028*100/(109) = 9200.

IN THIS METHOD, Since, 10028 includes (3%+9%+down payment) people is making 10028*100 is equal to cost and then 1002800/109, which automatically lead us to the amount 9200 which includes (3% interest + down payment).

Finally:10028*(100/109) = 9200.

2 Method: (Negative one):

IN THIS METHOD, people are finding the down payment first by doing 10028*(100/112), then finding the interest for 3 months
8953.57*(12%)*(3/12) and adding them.

Finally:10028*(100/112)*(103/100) = 9222.17

IN 2nd method the whole interest is taken out first then it applied for three month as 8953.57*(12%)*(3/12) = 8953.57*1.03.

Conclusion: Both the methods are right at their own places, but 1 method is much better as it do not have double effect and no by dividing 10028/109, we make appropriately, but this figure is approximately calculated as both of 109 and 103 figs has gotten disturbed 8953.57*1.03.

RULE: Only! The total amount is divided by unnecessary Figure to get to the required figure.

Please try to prove the formula for P.W.

What is the correct answer?

Anyone, please explain.

In this question if we are taking money.that mean u have to pay for whole period and in this question he paid s.i. monthly.so he want to settle after 3 months....remaining month is 9.it means he will pay for 9 month completely.
10028-x=(x*12*(9/12))/100;
the value of x=9200
am i correct?

How answer comes 9200? I have tried in my calculator but it show me 3963. 63, How could this possible, please can any one post here.