The smart metering infrastructure in Sweden allows electricity providers to offer electricity RTP (real time pricing) to homeowners, together with other dynamic pricing contracts across the country. These contracts are supposed to encourage users to shift power consumption during peak hours to help balance the load in the power system. Of all the available contracts in Sweden, monthly-average price holds the largest share, in response to the low electricity prices during the last three years. It is not clear if RTP will become a popular dynamic pricing scheme since daily price fluctuations might keep customers away from this type of contract. Literature review suggests that RTP adoption is only beneficial when combined with the use of customer demand flexibility, but it does not provide enough information about users adopting RTP without changing their electricity usage profile. This paper studies the economic impact if customers would shift to RTP contracts without adopting demand-side management. To achieve this, electricity costs from a large group of households were calculated and compared between both pricing schemes using the hourly consumption data of a 7-year period. Results suggest that the RTP electricity contract offer a considerable economic savings potential even without enabling consumer demand-side management.