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Cash accumulation equation : ウィキペディア英語版
Cash accumulation equation

The cash accumulation equation is an equation which calculates how much money will be in a bank account, at any point in time. The account pays interest, and is being fed a steady trickle of money.
== Compound interest ==
We will approach the development of this equation by first considering the simpler case, that of just placing a lump sum in an account and then making no additions to the sum. With the usual notation, namely
the equation is
and so the sum of money grows exponentially. Differentiating this we derive
and applying the definition of from eqn (1) to eqn (2), yields
Note that eqn. (1) is a particular solution to the ordinary differential equation in eqn. (3), with equal to at .

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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