Aptitude - True Discount - Discussion

I think philosophical debate can be done on this question. Cos logic regarding both answers are attractive.

For Rs. 50 gain : Time value of Rs. 2200 at 10% discount rate spanning over 1 year is 2000 (NPV=FV(1+i/100)). So its a gain of Rs. 50.

For Rs. 55 gain : The seller has invested Rs 1950 for one year at a rate of interest of 10% over 1 year span. So he is supposed to gain Rs. 195 at the end, but he would gain Rs. 250 so extra gain of Rs. 55.

Now we have to keep in mind that both calculations are virtual and depends on viewpoint of individual. Now think this problem another way - suppose the buyer (who is to pay Rs. 2200 after 1 year ) thinks to keep the money aside for future ease and engages somewhere at 10% interest rate for 1 year would have to bear Rs. 1980 out of his pocket and so he gets the same watch after 1 year with only Rs 30 extra cost but he has to sacrifice liquidity of Rs 2200 for one year.

Finally time value of money is always associated with investment. Here the tangible investment is Rs 1950 only and it will yield Rs. 2145 after 1 year at 10% rate and will make a gain of Rs. 55 to the "SELLER". And in pro-rate basis Rs 2200 is as good as Rs 2000 w.r.t "BUYER".

So what say?

if we think what profit he has made now and work with current values, we get the answer as 50.

If we work with future value (after 1 year, we get the answer as Rs 55). When we go with the method where we find current value of 2200 and get the value to be 2000, we see a profit of Rs 50. Here we are comparing the values in present time.

When we go with the method of applying 10% interest to 195, we compare both the values after a year.

So the profit he has made as per the current value is 50, but as per future value, it's 55.
and this justified by the fact that present value of Rs.55 after an year is Rs 50 (50 X 1.1 = 55).

The question isn't clear whether we have to determine profit on the basis of present value or value after an yer, so we assume by default that we have to calculate profit based on present values, in which case the answer is 50.

The question is bit ambiguous and so all these confusion. The question can either be what's the gain at present value or at end of one year. If it is at present value, we need to discount Rs. 2200 with 10% discounting rate to find out its present value - formula is PV = FV / (1+r)^n i.e., Present Value = 2200 (1+0.10)^1 = Rs. 2000 and so the gain would be Rs. 50.

If it is at the end of one year, Rs. 1950 + 10% would be Rs. 2145 and the gain would be Rs. 55 at the end of one year. Discounting Rs. 55 gain at the rate of 10%, you would get again Rs. 50 present value. So it depends on whether one would like to find out the gain at present value or the value at the end of one year.

It's better to frame the question like this without any ambiguity.

If we take interest on Rs 2200 how can he ever face a loss cuz he is selling at Rs 2000 that means he is already selling at a profit on which he is gaining the interest profit as well. If you take in that way the profit will become 250. 50 Rs on selling the difference between buying and Selling cost and the Rate of Interest money as well.

Instead the questions wants to see that he sold that Rs 2200 at a credit of 1 year and the general annual interest rate is 10% so did he make a loss or profit by selling it rather than gaining interest on it. Hence the 10% should be calculate at 1950 and then check with 2200 if he made a profit or loss.

Hence 55 comes as the correct answer.

Here's my take on this:

1) By default:

Begin Year 1, he bought a watch for 1950.

End Year 1, he sold it for 2200.

2) If he deposited in a bank, he got a 10% interest:

Begin Year 1, he deposited 1950.

End Year 1, he withdrawn all out and got 1950*1.1 = 2145.

=> So at the end of year 0, he gained 2200-2145 = 55.

I don't think the author of the question intend for it as a Present Value type. The 4 answers clearly said "gains/loses", it is simple present tense, which means he only "gains" the money at the end of year 1.

He cannot gain any money when we calculate PV at the Begin of year 1, because he has not bought the watch or deposited the money yet!

Guys, this is just the matter of point of time.

Simply:.

Income = 2200 - 1950 = 250.
Interest to pay = 1950 * 10% = 195.
Net profit = 250 - 195 = 55 (I believe this is the correct one in common sense).
However, in financial term, if we consider the net profit at t = 0 (at year 0, exactly when the man took the credit) instead of t = 1 (when the man sells the watch), we need to discount the net profit by 10% (which is a discount rate for the loss of money value in general) and we have: 55/ (1 + 10%) = 50.

The que actually is that the man buy the watch in Rs 1950 and sells it in 2200 in one yr.

But actually the rate of interest applies that time is 10%p.a. So if calculate the interest gain by guy due to dis rate, it will come out to be

c.p*r*t/100 =1950*10*1/100=195rs.

So actually the value of watch will be 1950+195=2095rs after one yr and the man sells it in rs.2200 .so clearly he gains a profit of RS 55 in 1 year.

I think this is correct according to the concept of the prob. without any formula.

Hi Saurabh/everybody,

This is what I also did earlier, But then, What you are wrong is considering 10% interest on the cost price which is wrong, Since he is not investing 1950 for 1 year but his current selling price 2000, Which is agreed over a period of 1 year.

He gains 10% on this current sp, which accumulate to 2200 over 1 year. So current selling price is 2000(with a simple interest calculations you can arrive at this figure). And hence he gains 50 rs from his current cost price of 1950.

Let's clear it up. Say the seller is S and buyer is B.

So S bought the watch for Rs.1950. Now B said he wanted to buy the watch. S gave the selling price as Rs.2200. B bought the watch from S at Rs.2000 and asked S to keep those Rs.2000 at a bank for 1 year at 10% interest. That way after 1 year, S will get his Rs. 2200.

So, at present S made a profit of only Rs.50 although after 1 year the overall profit will stand out to be Rs.250.

This seems correct.

Please correct me if I'm wrong.

Ok let me make this clear to all.

The man bought it at Rs. 1950 now.

The question literally means that at the end of 1 year, the man got Rs. 2200.

So Rs. 2200 is the amount.

Amount = P+SI.

2200 = P + P*R*T/100.

2200 = P + P*10*1/100.

2200 = P + 0.1 P.

Deducing from here comes P (The sum of money which the man could have got in terms of cash 1 year ago) = Rs. 2000 which is Rs. 50 (2000-1950) more than the cost price of the product (Rs. 1950).