Calculating Real Budget Deficit, given Nominal Deficit and Inflation

Question

I am doing this course on Coursera. In the context of explaining what Budget Deficits are, the professor puts up the following formula:

Real Deficit = Nominal Deficit - (Inflation*Total Debt)

My confusion is, where is the Total Debt coming from? Shouldn't Real Deficit be just a function of Nominal Deficit and Inflation? i.e.,

Real Deficit = Nominal Deficit - (Inflation*Real Deficit)

My understanding is that Total Debt is just the accumulated debt over the years (including the current year's budget deficit incurred so far). Is that understanding wrong?

The professor goes on to give a numerical example to explain the concept of inflating the debt. That's when the effective burden of debt falls due to inflation.

If Nominal Deficit = \$100 billion, inflation =10% and Total Debt = $5 trillion, then

Real Deficit = 100 - (0.10*5000) = -$800 billion.

I don't get it.

Edit: This is the direct link to the 6 minute lecture where he talks about it.

Answer 1

Basically the argument is that if in year $t$ deficit was 100mil but the same year the total debt 5billion and inflation was 10% that means that in real terms the value of debt is 500mill less and the teacher of that course treats this as 500mill revenue so under that definition even though you had 100mill deficit you would end up with 400mill surplus because thanks to inflation the net real debt decreased.

However, I must say it’s quite unusual to define real deficits in this way (see Barro’s Macroeconomics).