# Calculate present value for a recurring income

Say I have a recurring annual income of "i", it is annually readjusted by the interest of "r". The discount rate is "d". What is the formula to get the net present value assuming this income never ends?

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In year $n$ you receive $i(1+r)^{n-1}$, which is worth $i(1+r)^{n-1}(1-d)^{n-1}$. This is a geometric series with sum $\frac {i}{1-(1+r)(1-d)}$ assuming $d \gt r$. Otherwise the sum diverges to $\infty$. This assumes you start counting with this year as year $1$. You should check for offsets of $1$ depending on whether the income is at the start or end of the year and when the increase/discount is applied.