Expense and Balance Mismatch

There is no reason why the sum of the sequentially diminishing balance amounts should total the original amount.

To see why it is absurd to expect so, consider the example of sequentially spending $1$ rupee at a time:

Spend$\quad$Balance
$0\qquad\qquad 100$
$1\qquad\qquad 99$
$1\qquad\qquad 98$
$\;\vdots \qquad \qquad \;\vdots$
$1 \qquad \qquad 1$
$1\qquad \qquad 0$

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$100\qquad \quad 99 + 98 + \cdots 2 + 1 = 99\cdot 50 = 4950 \neq 100$

In the above example, the sum of the intermediate balance amounts greatly exceeds the starting balance of $100$.

In the following example, the sum of the intermediate balance is much less than the starting balance of $100$ rupee:

Spend$\quad$Balance
$0\qquad\qquad 100$
$99\qquad\qquad 1$
$\;\,1\qquad\qquad \,0$

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$100\qquad \quad 1 \neq 100$

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The important thing is to note that we must only have:

$$\text{Sum of amounts spent}\; = \;\text{Starting balance}\;-\;\text{Ending balance}$$