Humans don't understand the accumulation of small numbers - what is this phenomena called? I find that if you tell someone to give you 20$ vs. giving you 1$ everyday for 20 days - people react differently.

Similarly humans have a hard time comprehending the fact that small changes in their behaviour everyday may eventually lead to big consequences.
Humans have loads of cognitive biases. 

The one you have in mind could either be so called 'denomination effect', the tendency to care about large currency denominations and be less careful with smaller currency denominations. For example, not to care about the .99 part in a US 9.99 price tag.

It could also be the less-is-better effect. Small amounts of something are preferred than one big lump-sum. For example, buying something in 10 installments of US 110 is chosen instead of one scary US 1000 price tag.