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	Categories: Financial mathematics Accumulation function The accumulation function a(t) is a function defined in terms of time t expressing the time value of money. It is used in interest theory . The accumulation function assumes the initial investment to be 1. To obtain value of money where the initial investment is k, simply have $A(t) = k \cdot a(t)$ . The accumulation function has the following two properties: $a (0) = 1.$ It is an increasing function, in most cases, because interest are rarely negative. Common accumulation functions The accumulation function for the two common types of interest: Simple Interest $a(t)=1+t \cdot i.$ Compound Interest $a (t) = (1 + i) t .$ Categories: Financial mathematics

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