Marcus, named after Goldman’s co-founder, was launched two weeks ago offering savers an annual equivalent rate of 1.5%, including a 12-month bonus rate of 0.15%, on up to £250,000.
It was the highest easy-access rate on offer when it rolled out across the UK, putting pressure on the largest British banks that are already facing tough competition from smaller lenders.
On Tuesday, Goldman revealed that it has had 50,000 customers sign up to the retail bank since its launch.
RBS said its instant access savings account will pay the same annual rate but only up to the first £10,000, after which it will offer a rate of 0.2%.
For balances between £50,000 and £100,000, the bank will offer a rate of 0.85%.
The announcement comes as RBS tries to repair its reputation after a series of scandals related to misconduct and a £45.5bn government bailout during the height of the financial crisis in 2018.
Chairman Sir Howard Davies told The Times this week that the bank was considering changing the RBS brand to help revive its image.
Davies said the damage to the bank’s image from the government bailout and the years of financial struggles that followed had been “very serious”.