Returning with solution in hand

My beginning, as you may see,
has a unit of account.
That it does take first parts for me
is clearly paramount.

My middle, for writing refined,
is a symbol for its correction.
If you look, then you may just find
something unwieldy on inspection.

My ending, maybe drawn by horses,
carries people to and fro.
Travelling all the city courses,
its color now, is yellow.

My whole is returning -
the solution's in hand.
Are you quite discerning?
Then you may understand.

Who am I?

You are:

BACKWARDS!

My beginning, as you may see,
has a unit of account.
That it does take first parts for me
is clearly paramount.

Original answer: In finance, a DRAW is a transaction involving the movement of money from an account (hence 'withdraw' or 'overdrawn').

However: as pointed out in comments the OP's intention was SDR (Special Drawing Rights) which according to Wikipedia are "supplementary foreign exchange reserve assets defined and maintained by the International Monetary Fund. SDRs are units of account for the IMF, and not a currency per se."

My middle, for writing refined,
is a symbol for its correction.
If you look, then you may just find
something unwieldy on inspection.

The abbreviation AWK is used when marking essays or a transcript, to signify a sentence that does not flow smoothly (i.e. is 'unwieldy').

My ending, maybe drawn by horses,
carries people to and fro.
Travelling all the city courses,
its color now, is yellow.

This is indeed a CAB, as discovered by @trolley813 - something traditionally drawn by horses but famously yellow in the context of New York's taxicabs.

My whole is returning -
the solution's in hand.
Are you quite discerning?
Then you may understand.

Altogether, SDR + AWK + CAB spells SDRAWKCAB - but in reverse(!) ('returning') this spells (appropriately) BACKWARDS!

• rot13(Fcrpvny Qenjvat Evtugf (FQE) ner n havg bs nppbhag), but you got the gist of the answer already - please revise the answer to take this into account. – Avi Jan 23 at 20:12
• @Avi Ah yes, that's nice - 3 groups of 3 letters! Change made! – Stiv Jan 23 at 20:58

Are you

a taxicab?

My beginning, as you may see,
has a unit of account.
That it does take first parts for me
is clearly paramount.

TAX (taxes are accounted and important to pay)

My middle, for writing refined,
is a symbol for its correction.
If you look, then you may just find
something unwieldy on inspection.

unsure, maybe a reference to a Greek letter XI ($$\xi$$), which is somewhat beautiful and hard to write

My ending, maybe drawn by horses,
carries people to and fro.
Travelling all the city courses,
its color now, is yellow.

CAB (initially a horse-drawn carriage, now mostly yellow-coloured car)

My whole is returning -
the solution's in hand.
Are you quite discerning?
Then you may understand.

Probably a reference to the previous stanza (i.e. cab (or taxicab) was mentioned earlier and now returns)

• This isn't it, but you did get one part right :) – Avi Jan 23 at 19:21

The believe you are:

The Sun

My beginning, as you may see, has a unit of account. That it does take first parts for me is clearly paramount.

The unit of account is sunrise, the start of a day, the beginning that you may see. A sun rise if quite paramount to the entire day!

My middle, for writing refined, is a symbol for its correction. If you look, then you may just find something unwieldy on inspection.

The middle, the symbol, would be noon. The sun is at its peak and if you look at it, it is quite unwieldy! Literally.

My ending, maybe drawn by horses, carries people to and fro. Travelling all the city courses, its color now, is yellow.

Watching horses ride into the yellow sunset, the rays of sunshine travel the city streets before the sun completely sets.

My whole is returning - the solution's in hand. Are you quite discerning? Then you may understand.

The whole references the sun returning beyond the horizon after it has set!

• A creative interpretation, but unfortunately incorrect - each stanza is taken a little more literally. – Avi Jan 23 at 19:30