Solution:

63.984375

Explanation:
This question is hypothetical because you cannot transact in fractions in bank account. The following is the solution:

Year Amount Interest and Deduction
Start 63.984375
Y1 End 62.968750 63.984375 * 2 - 65
Y2 End 60.937500 62.96875* 2 - 65
Y3 End 56.875000 60.9375 * 2 - 65
Y4 End 48.750000 56.875 * 2 - 65
Y5 End 32.500000 48.75 * 2 - 65
Y6 End 0.000000 32.5 * 2 - 65 = 0

Solution:

The brain teaser can be solved as shown in the image below.

Solution:

The woman started walking across the bridge when the guard was inside the hut. She walked all the time he was inside (5 minutes) and then turned and moved back towards the kingdom. On approaching the kingdom he was asked for papers and since she did not have any, she was sent back.

Solution:

Michelangelo juggles the diamonds across while crossing the bridge.

Solution:

On Your lap.

Solution:

You will ask, I have a number in my mind that i.e. either 2 or 3. Is the number that I have in my mind smaller or equal to the number that you are thinking of?

If Alan replies with no, he is thinking of the number 1.
If Alan replies with yes, he is thinking of the number 3.
If Alan replies with don't know, he is thinking of the number 2.

Solution:

The clerk said that every day the password is CHANGED. Changed is the password.

Solution:

Zouma is 3 and has two footballs.
Ake is 1 and has one football.
Kalas is 4 and has three footballs.
Aina is 2 and has four footballs.

Solution:

Shikhar hit a sixer and then got retired hurt.
Suresh Raina came but he got run out after he and Kohli had crossed halfway.
On the next ball, Kohli scored a six and was not out at 100.

Solution:

I + IX = X

The equation read from the other side becomes X = XI + I which is false.

Solution:

Adam and Eve were the only people without navel. As they were not born out of a mother, they never had umbilical cords and thus never had navels.