What does it mean when a letter has both superscript and subscript?

Question

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 =

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

Answer 1

Depends on context, but in this case I think $R$ is an index (i.e., part of the name of the variable) and $T$ is an exponent.

Answer 2

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.

Answer 3

Let there be $A_1,A_2,A_3...$

And their squares are: $(A_1)^2,(A_2)^2,(A_3)^2...$

We don't need the parantheses: $A_1^2,A_2^2,A_3^2...$

Do you understand now?

$$\large A_b^c = (A_b)^c$$

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Do you know the quadratic formula?

Let $x_1$ and $x_2$ roots of $ax^2 + bx + c = 0$

Sum of squares of the roots ($x_1^2+x_2^2$) is equal to $(\frac{-b}{a})^2-\frac{2c}{a}$