Price Elasticity of Demand - elastic demand and impact of price reductions on total revenue A question in relation to Price Elasticity of Demand.

My understanding is that when demand is elastic, a price reduction will increase
total revenue.

If the price of a product changes from \$100 to \$80 (20% decrease) and quantity demanded increases from 1000 to 1240 (24% increase), PED = 24/-20 = -1.2 (elastic).

Total revenue at the original price (\$100) and quantity demanded (1000) = \$100,000 Total Revenue after the price change is \$80 x 1240 = \$99,200 so total revenue has actually fallen

Can anyone reconcile this with the point that when demand is elastic a price reduction should increase total revenue?
Like anything derived from calculus, the statement is guaranteed to hold true only for infinitesimal change. Unfortunately, since I don't know the entire demand function, I can't say much more than this.

A clear example of why this wouldn't work: starting at the same point \$100 and Q = 1000, we can decrease price to zero and total revenue would go down.