Question

why the modern currency is accepted as a medium of exchange

Answer 1

The modern currency is not made up of precious metal such as gold, silver or copper and unlike grain and cattle, they are neither every day use. Thus, the modern currency is without any use. ... Thus, modern currency is accepted as a medium of exchange without any use of its own.

Answer 2

The modern currency is not made up of any precious metal such as gold, silver or copper and unlike grain and cattle, they are neither every day use. Thus, the modern currency is without any use.
But still it is accepted as a medium of exchange as it is authorised by Government of the country.
In India, the Reserve Bank of India issues currency notes of India.