Interesting concept question

[VeryVeryCATy]

Ok, you must try to solve this question without formulae or calculations. It is a simple question based on the concept of percentage and interest:

A bank offers you a loan for 3 years with interest compounded annually. Except that, the rate of interest will be different in all 3 years. The 3 different rates of interest are 10%, 20%, and 30%. The bank allows you to choose the sequence of interest rates. For instance, you could say that I want to pay 10% in the 1st year, 20% in the 2nd, and 30% in the 3rd. Or you could say that I want to pay 30% in the 1st, 20% in the 2nd, and 10% in the third or any other sequence. Keeping in mind that interest is compounded annually, what sequence of interest should you choose? :rolleyes:

[Rajesh.Kannan]

Hmmm, interesting question. I think I know the answer, but I also see the trick in the question. Let me not spoil the fun by answering it right away. I see that you posted this less than 1 hour ago, so maybe I should wait till others have got the time to digest the question :D

[Ramki]

I should wait till others have got the time to digest the question

Totally digested dude. It does not matter what sequence you choose for the interest rates, right? In future, it would be great if you give the answer, and do not wait for our digestion :D

[Manish Salian]

Personally speaking I would choose the sequence 10%, 20% and 30%.

Let us say, I have borrowed 100 Rs.

In the first year I would pay, Rs.33.33 (Rs.100 / 3 years) plus an interest of 10% i.e. 10 Rs.

Since I have paid Rs.43.33 already, the next year I would pay interest on the remaining amont Rs.56.66.

The second year I would pay Rs.33.33 plus 20% of 56.66 (Rs.11.33) i.e. a net of Rs.44.66.

The third year I would pay an interest on only Rs.12.00 (56.66 - 44.66).

The third year payment would be Rs.33.33 plus 30% of 12 (Rs.3.60) i.e. a net of Rs. 36.93.

The total amount that I have paid = 43.33 + 44.66 + 36.93 = Rs.124.93

On the contrary, had I chosen the 30%-20%-10% scheme, I would have ended up paying much more (please calculate it yourself).

Having said that, for MBA entrance exams, the order does not matters :)

Now, have I managed to confuse you? :confused:

[Rajesh.Kannan]

Now, have I managed to confuse you? :confused:

You have managed to kill me :) Are you saying that if this question appeared in the CAT, I should say that all methods are the same?

[Ramki]

I think what Sir is trying to say is that the answer is "All choices are the same." However, in real life there are many other considerations such as payment of the principle thereby reducing the outstanding etc.