[Math] What does it mean when a letter has both superscript and subscript

financenotation

I have a formula for Bond Valuation of a Level Coupon Bond, but I don't understand the notation. It looks like:

It's the bottom formula in the image below, starting with PV =

enter image description here

What does it mean when the A has both T and R next to it?

Best Answer

In the context it is clear that $A_R^T = \frac 1{1 + R} + \frac 1{(1+R)^2}+ ...\frac 1{(1+R)^T}$.

Which by geometric series = $\frac {1-(1+R)^{T+1}}{R}$

So I think in this case it is simply a double index. There are two values that determine $A$; they are $R$ and $T$ so we need two indexes to reference $A$. We could have used $A_{R,T}$ just as easily.

In my opinion, I'd have chosen $A_{R,T}$ notation as $A_R^T$ looks like $(A_R)^T$ which I first thought it was (and it still might turn out to be) in my comment.

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