Meaning of throwing "Saisen"

Abstract

At the beginning of the year, Japanese people have an event to worship at shrines and temples called the “Hatumoude”. At the first visit, we give thanks for the year and pray for the safety and peace of the new year. One of the actions to be taken at the time of this first visit is the action of "throwing" money.

This act is seen not only at the time of the first visit but also when asking God or Buddha to grant some wish.

It can be inferred that the so-called offering is not compulsory and is one of the voluntary actions of each individual. Where does this motive come from? Why do people throw money in front of the money box?