Are there other accumulation functions that holds $a(n-t)={a(n) \over a(t)}$? This might be a beginner's question regarding accumulation methods and their functions, but so far I have learned that compound interest satisfy 
$$a(n-t)={a(n) \over a(t)}$$
Which allows nice results such as 
$$s_{\bar{n}\rceil} = (1+i)^n a_{\bar{n}\rceil}$$
I also understand that the first property does not hold for simple interest.  But out of curiosity, are there accumulation functions that are not compound interests that holds the same property?  If so, does it show up in real life actuarial problems?

The only real rule of accumulation functions is that a(0)=1.  So any function that you can think of for which f(n-t) = f(n)/f(t) qualifies provided you define a(0)=1.  An easy one would be a(t)=e^k(t)^2.  I'm just a student so I don't know what comes up in practice though.  
