After the correction of tariffs, volumes of MoneyGram transfers increased by 30%. What are the main benefits of money transfers by MoneyGram? Cost. Today, it is most advantageous to the customer service of all the similar services. Thousands of businesses count on MoneyGram for payment services to move money and drive commerce. This is a trust that MoneyGram takes very seriously. Millions of families depend on MoneyGram to safely send money home or pay the bills.