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A simple query on google could have given you the answer... Let's define lumpsum q periodic contribution a y periods a periodic rate i $$q*(1+i)^y + a( ((1+i)^y-1) / i ) - a = f$$ Suppose we do not want an initial investment $q=0$. 2040 - 2016 = 24 years. As you want to know the monthly contribution, everything needs to be converted to months. Thus ...

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