# Bank doubles money in one year puzzle

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A man deposited an amount to the bank. In which his amount doubles in one year. But, Bank cut off 65 rupees after doubling the amount in one year. After 6th year doubling and charging 65, the amount became zero.

What is amount, he deposited to the bank?

The scenario is practically impossible, NOT just because there is no such bank, but because one can’t deposit amounts in fractions of paise.

Theoretically, though, this scenario is possible as below:

 Year Amount Calc. 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

Asumming an ideal world situation where amount can be deposited in paise.teh acc to qustion let the initial amount be x.
after the end of first year amount left=2*x-65
after second year amount left=2*(2*x-65)-65=4*x-(2^2-1)*65
after third year amount left=2*(2*(2*x-65)-65)-65=8*x-(2^3-1)*65
after fourth year amount left=2*(8*x-7*65)-65
similarly after nth year amount left=(2^n)*x-(2^n-1)*65
after Sixth year amount is =0;
(2^6)*x-(2^6-1)*65=0;
From this x=63.984375
clearly from the answer this is impossible in practical world.